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Concept in linear algebra
{\displaystyle A\in \mathbb {F} ^{m\times n}} , a rank decomposition or rank factorization of A is a factorization of A of the form A = CF, where C ∈ F m × r
Rank_factorization
Dimension of the column space of a matrix
(so-called rank-revealing QR factorization), which are still more numerically robust than Gaussian elimination. Numerical determination of rank requires
Rank_(linear_algebra)
Algorithms for matrix decomposition
non-negative matrix factorizations was performed by a Finnish group of researchers in the 1990s under the name positive matrix factorization. It became more
Non-negative matrix factorization
Non-negative_matrix_factorization
In linear algebra, relation between 3 dimensions
{\displaystyle r\times (n-r)} matrix B {\displaystyle \mathbf {B} } (see rank factorization) and, hence, A = ( A 1 A 1 B ) . {\displaystyle \mathbf {A} ={\begin{pmatrix}\mathbf
Rank–nullity_theorem
Techniques for lossy compression of neural networks
approximated by low-rank matrices. Let W {\displaystyle W} be a weight matrix of shape m × n {\displaystyle m\times n} . A low-rank approximation is W
Model_compression
Representation of a matrix as a product
discipline of linear algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices. There are many different
Matrix_decomposition
Computational method
In mathematics and computer algebra, factorization of polynomials or polynomial factorization expresses a polynomial with coefficients in a given field
Factorization_of_polynomials
Concept in linear algebra
An RRQR factorization or rank-revealing QR factorization is a matrix decomposition algorithm based on the QR factorization which can be used to determine
RRQR_factorization
Matrix decomposition method
In linear algebra, the Cholesky decomposition or Cholesky factorization (pronounced /ʃəˈlɛski/ shə-LES-kee) is a decomposition of a Hermitian, positive-definite
Cholesky_decomposition
Problem 73-14, Rank Factorization of Nonnegative Matrices", SIAM Review 16(3), 393-394, 1974 Berman, A., Plemmons, R.J.: "Rank Factorization of Nonnegative
Nonnegative rank (linear algebra)
Nonnegative_rank_(linear_algebra)
Type of matrix factorization
factorization (as mentioned above); infinitely many LU factorizations if any of the first (n − 1) columns are linearly dependent; no LU factorization
LU_decomposition
Matrix decomposition
In linear algebra, a QR decomposition, also known as a QR factorization or QU factorization, is a decomposition of a matrix A into a product A = QR of
QR_decomposition
Statistical principle
on one's inference about the population mean. Fisher's factorization theorem or factorization criterion provides a convenient characterization of a sufficient
Sufficient_statistic
Subfield of mathematical optimization
the set of all solutions can be presented as: Fz+x0, where z is in Rk, k=n-rank(A), and F is an n-by-k matrix. Substituting x = Fz+x0 in the original problem
Convex_optimization
Algebraic element satisfying some of the criteria of an inverse
provided A {\displaystyle A} has full column rank. If A = B C {\displaystyle A=BC} is a rank factorization, then G = C R − 1 B L − 1 {\displaystyle G=C_{\mathrm
Generalized_inverse
Subfield of convex optimization
nonlinear programming algorithm for solving semidefinite programs via low-rank factorization", Mathematical Programming, 95 (2): 329–357, CiteSeerX 10.1.1.682
Semidefinite_programming
Decomposition in multilinear algebra
algorithms: Power iteration Factorization Machines: Support Vector Machines (SVMs) and factorization Bayesian factorizations/Sampling/Markov Chain Monte
Tensor_rank_decomposition
Solving multiple machine learning tasks at the same time
that A is constrained to be a graph Laplacian, or that A has low rank factorization. However these penalties are not convex, and the analysis of the barrier
Multi-task_learning
Algorithm that estimates unknowns from a series of measurements over time
the U-D factorization uses the same amount of storage, and somewhat less computation, and is the most commonly used triangular factorization. (Early literature
Kalman_filter
The Tomasi–Kanade factorization is the seminal work by Carlo Tomasi and Takeo Kanade in the early 1990s. It charted out an elegant and simple solution
Tomasi–Kanade_factorization
Matrix decomposition
eigendecomposition (also known as eigenvalue decomposition or EVD) is a factorization of a matrix A {\displaystyle A} into a canonical form given by A =
Eigendecomposition of a matrix
Eigendecomposition_of_a_matrix
Method of data analysis
L1-norm principal component analysis Low-rank approximation Matrix decomposition Non-negative matrix factorization Nonlinear dimensionality reduction Oja's
Principal_component_analysis
Connectivity measure in graph theory
correspondence with the edges of G. If the cycle rank of the digraph G is at most k, then the Cholesky factorization of M can be computed in at most k steps on
Cycle_rank
Matrix equal to its transpose
non-negative entries. This result is referred to as the Autonne–Takagi factorization. It was originally proved by Léon Autonne (1915) and Teiji Takagi (1925)
Symmetric_matrix
Orthonormalization of a set of vectors
application of the Gram–Schmidt process to the column vectors of a full column rank matrix yields the QR decomposition (it is decomposed into an orthogonal and
Gram–Schmidt_process
Matrix decomposition
In linear algebra, the singular value decomposition (SVD) is a factorization of a real or complex matrix into a rotation, followed by a scaling, followed
Singular_value_decomposition
Branch of number theory
arithmetic, that every (positive) integer has a factorization into a product of prime numbers, and this factorization is unique up to the ordering of the factors
Algebraic_number_theory
Type of matrix representation
decomposition of a square real or complex matrix A {\displaystyle A} is a factorization of the form A = U P {\displaystyle A=UP} , where U {\displaystyle U}
Polar_decomposition
Concept in machine learning
In 2009, the work of Sutskever introduced Bayesian Clustered Tensor Factorization to model relational concepts while reducing the parameter space. From
Tensor_(machine_learning)
Discrete Fourier transform algorithm
factorize the DFT similarly to Cooley–Tukey but without the twiddle factors. The Rader–Brenner algorithm (1976) is a Cooley–Tukey-like factorization but
Fast_Fourier_transform
Filling in missing entries of a matrix
to factorization-based algorithms is Gauss–Newton Matrix Recovery (GNMR). Similar to alternating minimization, GNMR addresses the factorized low-rank matrix
Matrix_completion
Concept in mathematics
theorem states that the Lyndon words furnish a factorization. More generally, Hall words provide a factorization; the Lyndon words are a special case of the
Free_monoid
Algebraic structure
completely different for factorization: the proof of the unique factorization does not give any hint for a method for factorizing. Already for the integers
Polynomial_ring
Coordinate-free definition of a tensor
the tensor is nonzero and completely factorizable. Every tensor can be expressed as a sum of simple tensors. The rank of a tensor T is the minimum number
Tensor_(intrinsic_definition)
Positive integer of the form (2^(2^n))+1
Yves Gallot, Generalized Fermat Prime Search Mark S. Manasse, Complete factorization of the ninth Fermat number (original announcement) Peyton Hayslette
Fermat_number
Theorem classifying finite simple groups
about finite groups. However, a significant difference from integer factorization is that such "building blocks" do not necessarily determine a unique
Classification of finite simple groups
Classification_of_finite_simple_groups
Decomposition of an integer as a sum of positive integers
Integer partitions. Rank of a partition, a different notion of rank Crank of a partition Dominance order Factorization Integer factorization Partition of a
Integer_partition
Approximation method
results of matrix arithmetic operations like matrix multiplication, factorization or inversion can be approximated in O ( n k α log ( n ) β ) {\displaystyle
Hierarchical_matrix
Algebra with unique prime factorization
factors into a product of prime ideals. It can be shown that such a factorization is then necessarily unique up to the order of the factors. There are
Dedekind_domain
Algebraic construction
integers, every element has a factorization into irreducible elements, but the ring need not have the property of unique factorization: for example, in the ring
Ring_of_integers
Prime number in the Fibonacci sequence
Record Fibonacci primes at the Prime Pages Factorization of the first 300 Fibonacci numbers Factorization of Fibonacci and Lucas numbers Archived 2016-08-19
Fibonacci_prime
Natural number
Vinberg polytopes of rank n + 4 mirrors, where there is one unique figure with eleven facets. On the other hand, such figures with rank n + 3 mirrors exist
7
Extracting features from raw data for machine learning
Non-Negative Matrix Factorization (NMF), Non-Negative Matrix-Tri Factorization (NMTF), Non-Negative Tensor Decomposition/Factorization (NTF/NTD), etc. The
Feature_engineering
Statement in abstract algebra
uniquely decomposed in much the same way that integers have a prime factorization. The result provides a simple framework to understand various canonical
Structure theorem for finitely generated modules over a principal ideal domain
Structure_theorem_for_finitely_generated_modules_over_a_principal_ideal_domain
Natural number
4-dimensions. There are also 5 compact hyperbolic Coxeter groups, or 4-prisms, of rank 5, each generating uniform honeycombs in hyperbolic 4-space as permutations
5
Natural number
binary BBP-type formulae. 23 is the first prime p for which unique factorization of cyclotomic integers based on the pth root of unity breaks down. 23
23_(number)
Matrix of geometric progressions
method) to solve the equation in O(n2) time, which also gives the UL factorization of V − 1 {\displaystyle V^{-1}} . The resulting algorithm produces extremely
Vandermonde_matrix
Complexity class used to classify decision problems
problem in polynomial time. The decision problem version of the integer factorization problem: given integers n and k, is there a factor f with 1 < f < k
NP_(complexity)
American theoretical physicist
method in that regime. He also worked on reformulation and proof of factorization theorems with Stephen Libby, John C. Collins and Davison E. Soper. He
George_Sterman
Commutative ring with a Euclidean division
also a unique factorization domain and a Noetherian ring. With respect to general principal ideal domains, the existence of factorizations (i.e., that R
Euclidean_domain
Topics referred to by the same term
populations Quadratic sieve, an integer factorization algorithm Quality Score, a variable used by search engines to set the rank and cost of ads Quicksort, a sorting
QS
Process in algebra
Vasilescu, M.A.O.; Kim, E. (2019). Compositional Hierarchical Tensor Factorization: Representing Hierarchical Intrinsic and Extrinsic Causal Factors. In
Tensor_decomposition
Form of mathematical proof
Predicate functional variable propositional variable Proof Quantifier ∃ ! ∀ rank Sentence atomic spectrum Signature String Substitution Symbol function logical/constant
Mathematical_induction
Mathematical operation
square root may be used for any factorization of a positive semidefinite matrix A as BTB = A, as in the Cholesky factorization, even if BB ≠ A. This distinct
Square_root_of_a_matrix
Generalization of the Riemann zeta function for algebraic number fields
ζ ( s ) {\displaystyle \zeta (s)} represents information about the factorization of integers. Dedekind zeta functions generalize many properties of the
Dedekind_zeta_function
More equations than unknowns (mathematics)
does exist. However, to achieve good numerical accuracy, using the QR factorization of A to solve the least squares problem is preferred. The QR decomposition
Overdetermined_system
1-factorable. The perfect 1-factorization conjecture that every complete graph on an even number of vertices admits a perfect 1-factorization. Cereceda's conjecture
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
\mathbb {N} ^{k}} , called the degree map, which satisfy the following factorization property: if λ ∈ Λ {\displaystyle \lambda \in \Lambda } and m , n ∈
K-graph_C*-algebra
Algebraic curve in mathematics
find applications in elliptic curve cryptography (ECC) and integer factorization. An elliptic curve is not an ellipse in the sense of a projective conic
Elliptic_curve
Norm on a vector space of matrices
also called the γ 2 {\displaystyle \gamma _{2}} -norm, refers to the factorization norm: γ 2 ( A ) = min U , V : A = U V T ‖ U ‖ 2 , ∞ ‖ V ‖ 2 , ∞ = min
Matrix_norm
Linear algebra concept
Cambridge University Press. Povey, Daniel, et al. (2018). "Semi-Orthogonal Low-Rank Matrix Factorization for Deep Neural Networks." Interspeech. v t e
Semi-orthogonal_matrix
Field extension of the rational numbers by a primitive root of unity
{\displaystyle n} )—and more precisely, because of the failure of unique factorization in their rings of integers—that Ernst Kummer first introduced the concept
Cyclotomic_field
Topics referred to by the same term
integer factorization Pollard's rho algorithm for logarithms ρ, prime constant ρ, plastic ratio, a geometrical proportion ρ, Spearman's rank correlation
Rho_(disambiguation)
Multilinear extension of principal component analysis
tasks. Various extension of MPCA: Robust MPCA (RMPCA) Multi-Tensor Factorization, that also finds the number of components automatically (MTF) M.A.O
Multilinear principal component analysis
Multilinear_principal_component_analysis
Block design in combinatorial mathematics
matching with the factorization labels in turn. Similarly add three more blocks 12CDEF, 34CDEF, and 56CDEF, replacing the factorization labels by the corresponding
Steiner_system
American computer scientist and statistician
(PCA) for gene expression modeling, low-rank matrix completion for recommender systems, robust matrix factorization for video surveillance, and concentration
Lester_Mackey
octahedron with edgelength 20 1603 = number of partitions of 27 with nonnegative rank 1604 = number of compositions of 22 into prime parts 1605 = number of polyominoes
1000_(number)
Dimensionality reduction of graph-based semantic data objects [machine learning task]
Ivana; Allen, Carl; Hospedales, Timothy M. (2019). "TuckER: Tensor Factorization for Knowledge Graph Completion". Proceedings of the 2019 Conference
Knowledge_graph_embedding
Japanese supercomputer
benchmark is as follows: The solver method of choice is a combination of LU factorization and iterative refinement performed afterwards to bring the solution
Fugaku_(supercomputer)
Algorithm used by recommender systems
matrix[citation needed]. Therefore, similar to matrix factorization methods, tensor factorization techniques can be used to reduce dimensionality of original
Collaborative_filtering
Mathematics concept
Generating set of a group Presentation of a group Nielsen transformation, a factorization of elements of the automorphism group of a free group Normal form for
Free_group
Fundamental theorem in probability theory and statistics
exp(−(|x1|α + ⋯ + |xn|α)β) where α > 1 and αβ > 1. If β = 1 then f(x1, ..., xn) factorizes into const · exp (−|x1|α) ... exp(−|xn|α), which means X1, ..., Xn are
Central_limit_theorem
Probabilistic model
the properties of factorization and independences, but they differ in the set of independences they can encode and the factorization of the distribution
Graphical_model
(pseudo-)Riemannian manifold whose geodesics are reversible
B\right|_{{\mathfrak {m}}_{d}}} In certain practical applications, this factorization can be interpreted as the spectrum of operators, e.g. the spectrum of
Symmetric_space
American mathematician, cryptologist and computer scientist (born 1971)
integer factorization: a proposal". cr.yp.to. Arjen K. Lenstra; Adi Shamir; Jim Tomlinson; Eran Tromer (2002). "Analysis of Bernstein's Factorization Circuit"
Daniel_J._Bernstein
Regularization technique for ill-posed problems
classification with logistic regression or support vector machines, and matrix factorization. Since Tikhonov Regularization simply adds a quadratic term to the objective
Ridge_regression
Subset of artificial intelligence
Jason D. M. Rennie; Tommi S. Jaakkola (2004). Maximum-Margin Matrix Factorization. NIPS. Coates, Adam; Lee, Honglak; Ng, Andrew Y. (2011). An analysis
Machine_learning
Method of displaying stereoscopic images
such as computed tomography and non-negative matrix factorization and non-negative tensor factorization. Tools for the instant conversion of existing 3D
Autostereoscopy
Submodule of fractions in abstract algebra
integers O K {\displaystyle {\mathcal {O}}_{K}} is from being a unique factorization domain (UFD). This is because h K = 1 {\displaystyle h_{K}=1} if and
Fractional_ideal
Natural number
Model. Clifford algebras display a periodicity of 8. The Lie group E8 has rank 8, and is one of 5 exceptional Lie groups. The order of the smallest non-abelian
8
Type of Dirichlet series associated to number field extensions
showing some properties like existence of analytic continuation or factorization of Dedekind zeta functions by Artin L-functions. One of the main applications
Artin_L-function
3D display technology
parallax barriers: optimizing dual-layer 3D displays using low-rank light field factorization. Proc. of SIGGRAPH Asia 2010 (ACM Transactions on Graphics 29
HR3D
Computer-based method for summarizing a text
by latent semantic analysis (LSA) combined with non-negative matrix factorization (NMF). Although they did not replace other approaches and are often
Automatic_summarization
Natural number
Seventeen is the highest dimension for paracompact Vineberg polytopes with rank n + 2 {\displaystyle n+2} mirror facets, with the lowest belonging to the
17_(number)
Computer science data structure
binary representation of N and e2(N) is the exponent of 2 in the prime factorization of N. This is faster than a sequence of consecutive insertions into
Heap_(data_structure)
Algebra of formal sums
combination is its exponent in the factorization of a {\displaystyle a} , or the negation of its exponent in the factorization of b {\displaystyle b} . The
Free_abelian_group
Topological structure in number theory
complete Noetherian regular local ring, and in particular a unique factorization domain. It follows from the Weierstrass preparation theorem for formal
Iwasawa_algebra
List of unsolved computational problems
Is public-key cryptography possible? Log-rank conjecture Hartmanis–Stearns conjecture Can integer factorization be done in polynomial time on a classical
List of unsolved problems in computer science
List_of_unsolved_problems_in_computer_science
Mathematical algorithm
linear support vector machines (see LIBLINEAR) and non-negative matrix factorization. They are attractive for problems where computing gradients is infeasible
Coordinate_descent
Conjecture on zeros of the zeta function
have multiple complex zeros. This is because the Dedekind zeta functions factorize as a product of powers of Artin L-functions, so zeros of Artin L-functions
Riemann_hypothesis
Array of numbers
form. They are generally referred to as matrix decomposition or matrix factorization techniques. These techniques are of interest because they can make computations
Matrix_(mathematics)
Method in natural language processing
Matrix Factorization (PDF). NIPS. Li, Yitan; Xu, Linli (2015). Word Embedding Revisited: A New Representation Learning and Explicit Matrix Factorization Perspective
Word_embedding
Technique in machine learning
detection Reinforcement learning: Game-playing Graph learning Matrix factorization Guo, Sheng; Huang, Weilin; Zhang, Haozhi; Zhuang, Chenfan; Dong, Dengke;
Curriculum_learning
m\times n} matrix. This class of problem is associated with Rank revealing QR factorizations and D optimal experimental design. Minimal addition chains
List_of_NP-complete_problems
Polish computer scientist (born 1947)
Analysis (ICA), Non-negative matrix factorization (NMF), tensor decomposition, Deep (Multilayer) Factorizations for ICA, NMF, neural networks for optimization
Andrzej_Cichocki
German polymath and scholar (1777–1855)
clean presentation of modular arithmetic. It deals with the unique factorization theorem and primitive roots modulo n. In the main sections, Gauss presents
Carl_Friedrich_Gauss
Multivariable generalization of the Student's t-distribution
the standard representation is revealed by this formula, which does not factorize into the product of the marginal one-dimensional distributions. When Σ
Multivariate_t-distribution
Method of data analysis
Bouwmans; E. Zahzah (2012). "Foreground Detection via Robust Low Rank Matrix Factorization including Spatial Constraint with Iterative Reweighted Regression"
Robust principal component analysis
Robust_principal_component_analysis
Count of the possible partitions of a set
{\displaystyle N} . These are factorizations of N {\displaystyle N} into numbers greater than one, treating two factorizations as the same if they have the
Bell_number
Overview of and topical guide to machine learning
Multiple kernel learning Naive Bayes classifier Non-negative matrix factorization Online machine learning Out-of-bag error Prefrontal cortex basal ganglia
Outline_of_machine_learning
RANK FACTORIZATION
RANK FACTORIZATION
Boy/Male
Muslim
Respect, Rank
Boy/Male
English American
Military rank.
Girl/Female
Muslim/Islamic
From the arabic name Rani means queen. she is an energtic self-starter capable of sustaing a fast pace with strong leadership and qualities. a real motavater
Boy/Male
Muslim
Height. High rank.
Surname or Lastname
German, Dutch, Scandinavian, Slovenian, Czech, Hungarian, and Jewish (Ashkenazic)
German, Dutch, Scandinavian, Slovenian, Czech, Hungarian, and Jewish (Ashkenazic) : ethnic or regional name for someone from Franconia (German Franken), a region of southwestern Germany so called from its early settlement by the Franks, a Germanic people who inhabited the lands around the river Rhine in Roman times. In the 6th–9th centuries, under leaders such as Clovis I (c. 466–511) and Charlemagne (742–814), the Franks established a substantial empire in western Europe, from which the country of France takes its name. The term Frank in eastern Mediterranean countries was used, in various vernacular forms, to denote the Crusaders and their descendants, and the American surname may also be an Americanized form of such a form.English, Dutch, German, etc. : from the personal name Frank, in origin an ethnic name for a Frank. This also came be used as an adjective meaning ‘free’, ‘open-hearted’, ‘generous’, deriving from the fact that in Frankish Gaul only people of Frankish race enjoyed the status of fully free men.
Male
English
Pet form of English Henry, HANK means "home-ruler."
Female
Japanese
(è˜) Japanese name RAN means "lily" or "orchid."
Boy/Male
Indian
Respect, Rank
Male
Swedish
Variant spelling of Swedish Göran, JÖRAN means "earth-worker, farmer."
Male
Swedish
Swedish form of Greek Georgios, GÖRAN means "earth-worker, farmer."
Surname or Lastname
German, Dutch, and Jewish (Ashkenazic)
German, Dutch, and Jewish (Ashkenazic) : from Middle High German or Middle Low German banc, or Yiddish bank ‘bench’, ‘table’, ‘counter’, in any of various senses, e.g. a metonymic occupational name for anyone whose work required a bench or counter, for example a butcher, baker, court official, or money changer.Danish and Swedish : topographic name from bank ‘(sand)bank’ or a habitational name from a farm named with this word.Danish and Swedish : from bank ‘noise’, hence a nickname for a loud or noisy person. Compare Bang.Danish : habitational name from the German place name Bänkau.English : probably a variant of Banks.Americanized spelling of Polish Bąk, literally ‘horsefly’; perhaps a nickname for an irritating person.Hungarian (Bánk) : from a pet form of the old secular personal name Bán.
Boy/Male
Muslim/Islamic
High rank honour
Boy/Male
Indian
Respect, Rank
Male
English
 English name originally derived from the name of a Germanic tribe called the Franks, FRANK means "French." It is also used as a short form of Franklin "freeman" and Francis "French."Â
Surname or Lastname
English
English : nickname for a powerfully built man or someone of violent emotions, from the Middle English adjective rank (Old English ranc ‘proud’, ‘rebellious’).English : from a medieval personal name, a back-formation from the diminutive Rankin.South German : variant of Rang 2.German : nickname either for an agile person, from Middle High German ranc ‘quick turn’, or in some instances for someone who was tall and thin, from Low German rank. In some cases the surname may have been from a personal name formed with this element.Czech : from a pet form of a personal name, which could be either Slavic Ranožir or Germanic Randolf (see Randolph).Swedish and Danish : nickname from rank ‘erect’, ‘upright’, ‘straight’.
Female
Hindi/Indian
(रानी) Hindi name RANI means "queen."
Boy/Male
Muslim
Fame, Honor, High rank
Surname or Lastname
English
English : from the Middle English personal name Rand(e), a short form of any of the various Germanic compound personal names with the first element rand ‘(shield) rim’, as for example Randolph.English : topographic name for someone who lived on the margin of a settlement or on the bank of a river (from Old English rand ‘rim’, used in a topographical sense), or a habitational name from a place named with this word, as for example Rand in Lincolnshire and Rand Grange in North Yorkshire.German : from a short form of any of the various compound names formed with rand- ‘rim’. Compare 1.German : topographic name from Middle High German, Middle Low German rand, rant ‘edge’, ‘rim’.
Male
Hindi/Indian
Short form of Hindi Ranjeet, RANJ means "victorious in battle."
Boy/Male
Muslim
Respect, Rank
RANK FACTORIZATION
RANK FACTORIZATION
Girl/Female
French Greek American English
Flower.
Boy/Male
Tamil
One who is golden colored
Girl/Female
Tamil
Ariktha | அரிகà¯à®¤à®¾
Fulfilled
Boy/Male
Hebrew, Hindu, Indian
Brillance; Brightness; A Glow; Splendor
Girl/Female
Assamese, Hindu, Indian, Sindhi, Traditional
Possessing Gold
Boy/Male
Latin English Japanese
Of the Lord.
Boy/Male
Arabic
Wanted; Unknown
Boy/Male
Indian, Punjabi, Sikh
Blissful in God's Remembrance
Boy/Male
Hindu, Indian
Wearing Yellow
Boy/Male
Indian
Truth
RANK FACTORIZATION
RANK FACTORIZATION
RANK FACTORIZATION
RANK FACTORIZATION
RANK FACTORIZATION
n. & v.
Grade of official standing, as in the army, navy, or nobility; as, the rank of general; the rank of admiral.
superl.
Causing vigorous growth; producing luxuriantly; very rich and fertile; as, rank land.
v. t.
To take rank of; to outrank.
v. t.
To wash on a rack, as metals or ore.
n. & v.
Degree of dignity, eminence, or excellence; position in civil or social life; station; degree; grade; as, a writer of the first rank; a lawyer of high rank.
a.
A frame on which articles are deposited for keeping or arranged for display; as, a clothes rack; a bottle rack, etc.
v. i.
To have a certain grade or degree of elevation in the orders of civil or military life; to have a certain degree of esteem or consideration; as, he ranks with the first class of poets; he ranks high in public estimation.
superl.
Raised to a high degree; violent; extreme; gross; utter; as, rank heresy.
v. i.
To keep a bank; to carry on the business of a banker.
n.
A mound, pile, or ridge of earth, raised above the surrounding level; hence, anything shaped like a mound or ridge of earth; as, a bank of clouds; a bank of snow.
n. & v.
Elevated grade or standing; high degree; high social position; distinction; eminence; as, a man of rank.
n. & v.
A row or line; a range; an order; a tier; as, a rank of osiers.
n. & v.
An aggregate of individuals classed together; a permanent social class; an order; a division; as, ranks and orders of men; the highest and the lowest ranks of men, or of other intelligent beings.
v. i.
To deposit money in a bank; to have an account with a banker.
superl.
Strong-scented; rancid; musty; as, oil of a rank smell; rank-smelling rue.
v. t.
To deposit in a bank.
superl.
Luxuriant in growth; of vigorous growth; exuberant; grown to immoderate height; as, rank grass; rank weeds.
v. t.
To heap or pile up; as, to bank sand.
v. i.
To rant; to storm.
v. i. & t.
To become lank; to make lank.