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Matrix normal form
In mathematics, the Smith normal form (sometimes abbreviated SNF) is a normal form that can be defined for any matrix (not necessarily square) with entries
Smith_normal_form
Matrix form in linear algebra
Hermite normal form is an analogue of reduced echelon form for matrices over the integers Z {\displaystyle \mathbb {Z} } . Just as reduced echelon form can
Hermite_normal_form
Canonical form of matrices over a field
algebra, the Frobenius normal form or rational canonical form of a square matrix A with entries in a field F is a canonical form for matrices obtained
Frobenius_normal_form
Standard representation of a mathematical object
In mathematics and computer science, a canonical, normal, or standard form of a mathematical object is a standard way of presenting that object as a mathematical
Canonical_form
Polynomial equation whose integer solutions are sought
solved by computing the Smith normal form of its matrix, in a way that is similar to the use of the reduced row echelon form to solve a system of linear
Diophantine_equation
Commutative group (mathematics)
equivalent with multiplying M on the right by a unimodular matrix. The Smith normal form of M is a matrix S = U M V , {\displaystyle S=UMV,} where U and V
Abelian_group
Equivalence under a change of basis (linear algebra)
defines the characteristic polynomial). Note that this Smith normal form is not a normal form of A itself; moreover it is not similar to XIn − A either
Matrix_similarity
British mathematician (1826–1883)
quadratic forms, and Smith–Minkowski–Siegel mass formula in number theory. In matrix theory he is visible today in having his name on the Smith normal form of
Henry_John_Stephen_Smith
Form in relational database normalization
Sixth normal form (6NF) is a normal form used in relational database normalization which extends the relational algebra and generalizes relational operators
Sixth_normal_form
associatedness. The invariant factors of a matrix over a PID occur in the Smith normal form and provide a means of computing the structure of a module from a
Invariant_factor
Commutative group where every element is the sum of elements from one finite subset
needed] The finitely presented case is solved by Smith normal form, and hence frequently credited to (Smith 1861), though the finitely generated case is sometimes
Finitely generated abelian group
Finitely_generated_abelian_group
Algebraic structure associated with a topological space
computed by putting matrix representations of these boundary mappings in Smith normal form. Using simplicial homology example as a model, one can define a singular
Homology_(mathematics)
Representation of a game in game theory
In game theory, normal form is a description of a game. Unlike extensive form, normal-form representations are not graphical per se, but rather represent
Normal-form_game
Algorithmic runtime requirements for matrix multiplication
characteristic polynomial, eigenvalues (but not eigenvectors), Hermite normal form, and Smith normal form.[citation needed] In his 1969 paper, where he proved the complexity
Computational complexity of matrix multiplication
Computational_complexity_of_matrix_multiplication
Subfield of mathematical topology
application of the Smith form algorithm get filled-in even if one starts and ends with sparse matrices. Efficient and probabilistic Smith normal form algorithms
Computational_topology
Computer algebra system
sparse matrix, determinant, normalize, column reduce, row echelon, Smith normal form, and matrix inverse. It is consistently faster than some well known
Fermat (computer algebra system)
Fermat_(computer_algebra_system)
Statement in abstract algebra
generators), and put it in Smith normal form. This yields the invariant factor decomposition, and the diagonal entries of Smith normal form are the invariant factors
Structure theorem for finitely generated modules over a principal ideal domain
Structure_theorem_for_finitely_generated_modules_over_a_principal_ideal_domain
Algebra of formal sums
existence part of the theorem is provided by any algorithm computing the Smith normal form of a matrix of integers. Uniqueness follows from the fact that, for
Free_abelian_group
Probability distribution
a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of
Normal_distribution
Mathematical equivalence relation
diagonal is equal to k {\displaystyle k} . This is a special case of the Smith normal form, which generalizes this concept on vector spaces to free modules over
Matrix_equivalence
Matrix decomposition
decomposition Principal component analysis (PCA) Schmidt decomposition Smith normal form Singular value Time series Two-dimensional singular-value decomposition
Singular_value_decomposition
Diophantine equations. The original paper Henry John Stephen Smith that defined the Smith normal form was written for linear indeterminate systems. Hua, Luogeng
Indeterminate_system
Part of algebraic geometry devoted to the elimination of variables between polynomials
Diophantine equations and abelian groups with the Hermite normal form and Smith normal form. Before the 20th century, different types of eliminants were
Elimination_theory
Periodic set of points
{Z} )} with N M = I d n {\displaystyle NM=\mathrm {Id} _{n}} . The Smith normal form of M {\displaystyle M} has only 1's on the main diagonal. The maximal
Lattice_(group)
Topics referred to by the same term
programme), 2013–2016 Server Normal Format, a bitmap font format used by X Window Skilled nursing facility Smith normal form Spent nuclear fuel This disambiguation
SNF
Partition of space by a hyperplanes
[q]} ) for the arrangement and much information is contained in its Smith normal form. In complex affine space (which is hard to visualize because even
Arrangement_of_hyperplanes
Linear map over a ring
example of an additive relation. Mapping cone (homological algebra) Smith normal form Chain complex Pairing Bourbaki, Nicolas (1998), "Chapter II, §1.14
Module_homomorphism
Characteristic of undirected graphs
Schochetman, Irwin E. (1995), "On the minors of an incidence matrix and its Smith normal form", Linear Algebra and Its Applications, 218: 213–224, doi:10
Rank_(graph_theory)
British playwright and screenwriter
Susan Smith Blackburn Prize. Birch was also the screenwriter for the film Lady Macbeth and has written for such television shows as Succession, Normal People
Alice_Birch
Antagonist in The Matrix (film series)
voiced by Christopher Corey Smith in The Matrix: Path of Neo (2005), with Ian Bliss and Gideon Emery playing his human form, Bane, in the films and Path
Agent_Smith
Algebraic formula
repeat to find the invariant factors before it. Invariant factors Smith normal form B. Hartley; T.O. Hawkes (1970). Rings, modules and linear algebra
Elementary_divisors
is a nonzero module whose only submodules are zero and itself. Smith Smith normal form stably free A stably free module structure theorem The structure
Glossary_of_module_theory
Indie rock band
Normal is a two-piece indie rock band from Vancouver, British Columbia, Canada, formed by Jean Smith and David Lester in 1984. In 1985, they formed their
Mecca_Normal
American drummer (born 1961)
in 2012. Smith is also the drummer of the hard rock supergroup Chickenfoot, formed in 2008, and of the all-instrumental outfit Chad Smith's Bombastic
Chad_Smith
determinant of the square matrix is 1.) Having such an algorithm, the Smith normal form of a matrix may be computed exactly as in the integer case, and this
Linear_equation_over_a_ring
Generalization of the one-dimensional normal distribution to higher dimensions
normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization of the one-dimensional (univariate) normal distribution
Multivariate normal distribution
Multivariate_normal_distribution
American mathematician
GNU Free Documentation License, 2017. “A confused electrician uses Smith normal form,” with Tom Edgar. Mathematics Magazine 89(1) (2016), 3–13. Mathematics
Jessica_Sklar
Live-television incident in 2022
However, the show did not use hosts from this point and continued as normal. Smith's expletives were censored by audio muting during the live broadcast
Chris Rock–Will Smith slapping incident
Chris_Rock–Will_Smith_slapping_incident
Town in Illinois, United States
Normal is a town in McLean County, Illinois, United States. The population was 52,736 at the 2020 census. Normal is the smaller of two principal cities
Normal,_Illinois
Graphical technique in statistics
or the median of the corresponding order statistics. The normal probability plot is formed by plotting the sorted data vs. an approximation to the means
Normal_probability_plot
Canadian indie pop band
LP, Being So Normal. It was released in September 2017 on the Vancouver indie label Kingfisher Bluez. Vocalist/rhythm guitarist Neil Smith was formerly
Peach_Pit_(band)
This article lists forms of government and political systems, which are not mutually exclusive, and often have much in common. According to Yale professor
List_of_forms_of_government
Central concept in Marxian critique of political economy
the form of value established by the exchange of products. People know very well that any product represents a value, i.e. that there is a normal economic
Value-form
Normal school in Texas, United States
Markers". www.coloradocountyhistory.org. "Oakland Normal School". Texas Historical Markers. "Smith, Robert Lloyd | Encyclopedia.com". www.encyclopedia
Oakland_Normal_School
English rock band (1976–2018)
post-punk band, formed in 1976 in Prestwich, Greater Manchester. They had many line-up changes, with vocalist and founder member Mark E. Smith being the only
The_Fall_(band)
Educational institution to train teachers
societal values, ideologies and dominant narratives in the form of curriculum. The first public normal school in the United States was founded in Concord, Vermont
Normal_school
Semen discharge from the male reproductive tract
A vasectomy alters the composition of the ejaculate as a form of birth control. The normal precursor to ejaculation is sexual arousal of the male, leading
Ejaculation
Theory in classical and Marxian economics
value is determined by the average labor-time required for production under normal conditions. The development of the LTV from the late 17th century reflected
Labor_theory_of_value
Group of medical conditions characterized by irregular heartbeat
including when it is too fast or too slow. Essentially, this is anything but normal sinus rhythm. A resting heart rate that is too fast – above 100 beats per
Arrhythmia
Group of genetic connective tissues disorders
weakness. Some forms of EDS result in a normal life expectancy, but those that affect blood vessels generally decrease it. All forms of EDS can result
Ehlers–Danlos_syndrome
Mathematical models of strategic interactions
presented in extensive form. Every extensive-form game has an equivalent normal-form game, however, the transformation to normal form may result in an exponential
Game_theory
World record-setting British hydroplane
to relighting the engine in his commentary and then said: "relight made normal"". This was as K7 left the measured km, and the loss of engine thrust and
Bluebird_K7
Chemical element with atomic number 6 (C)
carbon allotropes are solids under normal conditions, with graphite being the most thermodynamically stable form at standard temperature and pressure
Carbon
Chemical compound
triphosphate (ATP), primarily in muscle and brain tissue. Its phosphorylated form, phosphocreatine, donates phosphate groups to adenosine diphosphate (ADP)
Creatine
Words of affirmation (yes) and negation or contradiction (no)
three-form or four-form systems. English originally used a four-form system up to and including Early Middle English. Modern English uses a two-form system
Yes_and_no
Liquid mixture produced by the vagina
development. Normal vaginal discharge may have a thin, watery consistency or a thick, sticky consistency, and it may be clear or white in color. Normal vaginal
Vaginal_discharge
Medical condition
be mistaken with normal nocturnal sexual behaviors, which do not occur during NREM sleep. Sexual behaviors that are viewed as normal during sleep and
Sleep_sex
Alexander McCall Smith. Bertie, "an endearing 7-year-old boy," has been described as the "most beloved character" in McCall Smith's novels. Bertie is
Bertie_Pollock
Thin plate with a hole, normally used to distribute the load of a threaded fastener
flat washers. Form A: Normal diameter, normal thickness Form B: Normal diameter, light thickness Form C: Large diameter, normal thickness Form D: Large diameter
Washer_(hardware)
Business process improvement technique
originates from statistical quality control, a reference to the fraction of a normal curve that lies within six standard deviations of the mean, used to represent
Six_Sigma
2023 film by Neil Burger
psychological thriller film directed by Neil Burger and written by Elle Smith and Mark L. Smith, based on the 2017 novel of the same name by Karen Dionne. It stars
The_Marsh_King's_Daughter
Eighth letter of the Greek alphabet
GREEK CAPITAL THETA SYMBOL, which differs from most realizations of the normal textual uppercase letter by having a cross-bar that goes all the way across
Theta
often providing intel to the ninja when required. Initially, he lacks normal social skills, such as a sense of humor, but it is later revealed that Zane
List_of_Ninjago_characters
Chemical reaction
central ring can form a 9,10 adduct with maleic anhydride at 80 °C and even with acetylene, a weak dienophile, at 250 °C. In a normal demand Diels–Alder
Diels–Alder_reaction
Abnormal yellowish skin colour caused by high level of bilirubin
(above 10), some other form of liver damage (above 1), or hepatitis (less than 1). Bilirubin levels greater than 10 times normal could indicate neoplastic
Jaundice
Decreased ability to see color or color differences
and perceptually uniform to all forms of color vision. Color blindness is any deviation of color vision from normal trichromatic color vision (often
Color_blindness
List of characters in the Rick and Morty franchise
Sanchez, an eccentric, alcoholic scientist who takes his grandson Morty Smith on dangerous, outlandish adventures throughout the cosmos and alternate
List of Rick and Morty characters
List_of_Rick_and_Morty_characters
Medical condition caused by receiving too little or too many nutrients
protein and other nutrients which adversely affects the body's tissues and form. Malnutrition is a category of diseases that includes undernutrition and
Malnutrition
Form of arthritis causing swollen joints
fluid or in a deposit outside the joint. Blood uric acid levels may be normal during an attack. Treatment with nonsteroidal anti-inflammatory drugs (NSAIDs)
Gout
Physical quantity
and in the form of heat and light. Energy is a conserved quantity—the law of conservation of energy states that energy can be converted in form, but not
Energy
Plane curve
Hesse normal form of a line to calculate the distance | P l | {\displaystyle |Pl|} .) An ellipse possesses the following property: The normal at a point
Ellipse
United States Army general (1885–1945)
George Smith Patton Jr. (11 November 1885 – 21 December 1945) was a general in the United States Army who commanded the Seventh Army in the Mediterranean
George_S._Patton
Computer storage device with no moving parts
and standard HDD form factors allow such SSDs to be used as drop-in replacements for HDDs in computers and other devices. Newer form factors such as mSATA
Solid-state_drive
pleasure, etc.) the players are allocated by the end of the game. A game in normal form is a function: π : ∏ i ∈ N Σ i → R N {\displaystyle \pi \ :\prod
Glossary_of_game_theory
Third planet from the Sun
surface temperature of 14.76 °C (58.57 °F), at which water is liquid under normal atmospheric pressure. Differences in the amount of captured energy between
Earth
Integral equation
time t {\displaystyle t} n {\displaystyle \mathbf {n} } is the surface normal at x {\displaystyle \mathbf {x} } ω i ⋅ n {\displaystyle \omega _{\text{i}}\cdot
Rendering_equation
Toxic effects of breathing oxygen at high partial pressures
of oxygen by one or two electrons to form reactive oxygen species, which are natural by-products of the normal metabolism of oxygen and have important
Oxygen_toxicity
Sexual stimulation of one's own genitals
a medically healthy and psychologically normal habit. No causal relationship between masturbation and any form of mental or physical disorder has been
Masturbation
Species of mite
the skin environment caused by rosacea is more hospitable to mites than normal skin, allowing them to flourish. Populations of D. folliculorum are higher
Demodex_folliculorum
2004 novel by Alexander McCall Smith
44 Scotland Street is an episodic novel by Alexander McCall Smith, the author of The No. 1 Ladies' Detective Agency. The story was first published as
44_Scotland_Street
Condition in which the head is small due to an underdeveloped brain
κεφαλή kephalé "head") is a medical condition involving a smaller-than-normal head. Microcephaly may be present at birth or it may develop in the first
Microcephaly
Sensual art genre involving tentacles or pseudopods
sensual scene in bed. I thought I should do something to avoid drawing such a normal sensual scene. So I just created a creature. His tentacle is not a penis
Tentacle_erotica
Form of literature
Poetry (from the Greek word poiesis, "making") is a form of literary art that uses aesthetic and often rhythmic qualities of language to evoke meanings
Poetry
Conspiracy theory about contrails
the general public. Believers in this conspiracy theory say that while normal contrails dissipate relatively quickly, contrails that linger must contain
Chemtrail_conspiracy_theory
Normal schools in the United States in the 19th century were developed and built primarily to train elementary-level teachers for the public schools. The
Normal schools in the United States
Normal_schools_in_the_United_States
Microorganisms present in the vagina
Klebanoff SJ, Young-Smith K, Critchlow CM, Holmes KK (February 1989). "Prevalence of hydrogen peroxide-producing Lactobacillus species in normal women and women
Vaginal_flora
Perception of meaningful patterns or images in random or vague stimuli
messages in recorded music played in reverse or at higher- or lower-than-normal speeds, and hearing voices (mainly indistinct) or music in random noise
Pareidolia
Hypothetical life with reversed molecular chirality
acids Mirror matter – A hypothetical form of matter that interacts only weakly with normal matter, which could form mirror planets, potentially inhabited
Mirror-image_life
American author and cystic fibrosis advocate
had colonized Smith's lungs, including a form of Burkholderia cenocepacia which mutated over a decade of antibiotic treatment from a normal vegetable bacteria
Mallory_Smith
Species of salamander
axolotls at Vancouver Aquarium are leucistic, with less pigmentation than normal. Axolotls in a pet store in Melbourne, Australia Axolotls in a pond with
Axolotl
Condition in which organs are reversed
the major visceral organs are reversed or mirrored from their normal positions. The normal arrangement of internal organs is known as situs solitus. Many
Situs_inversus
Neuromuscular disease
life-threatening, the degree of disability can vary. Some people may live relatively normal lives with mild symptoms, while others may require orthopedic supports,
Charcot–Marie–Tooth_disease
Predatory hornet, largest in the world
lure/attractant development and molecular genetics research, both as part of its normal research mission, but also to further the near-term eradication goal in
Asian_giant_hornet
Video game character
faster, and jumps farther, but loses one ring per second and reverts to normal when his rings are depleted. Sonic CD, released in 1993, introduced Sonic's
Sonic the Hedgehog (character)
Sonic_the_Hedgehog_(character)
Propagating disturbance
orthogonal direction to the oblique shock as a normal shock. When an oblique shock is likely to form at an angle which cannot remain on the surface,
Shock_wave
Small size of an organism, caused by growth deficiency or genetic mutations
torso are unusually small. Intelligence is usually normal, and most people with it have a nearly normal life expectancy. People with dwarfism can usually
Dwarfism
Leader of China from 1949 to 1976
become a teacher and enrolled at the Fourth Normal School of Changsha, which soon merged with the First Normal School of Hunan, widely seen as the best in
Mao_Zedong
2001 film by Keenen Ivory Wayans
spirit of Kane's wife, and attempts to seduce Oldman, but quickly returns to normal with no memory of the event. A toy clown attempts to kill Ray, but in a
Scary_Movie_2
both back to normal. The skunk is revealed in his true form to be a normal man, who thanks Mordecai and Rigby for helping him return to normal, before passing
List of Regular Show characters
List_of_Regular_Show_characters
2013 American science fiction film by M. Night Shyamalan
details, such as Jaden Smith's character in the far distance, somehow looked clearer than I would have expected under normal circumstances; I got the
After_Earth
SMITH NORMAL-FORM
SMITH NORMAL-FORM
Boy/Male
Hindu
Devine smile
Male
English
English form of Teutonic Nordemann, NORMAN means "northman."
Boy/Male
American, British, Christian, English, Indian, Jamaican
Tradesman; Blacksmith; Smile
Surname or Lastname
English, Irish (Ulster), Scottish, and Dutch
English, Irish (Ulster), Scottish, and Dutch : name applied either to a Scandinavian or to someone from Normandy in northern France. The Scandinavian adventurers of the Dark Ages called themselves norðmenn ‘men from the North’. Before 1066, Scandinavian settlers in England were already fairly readily absorbed, and Northman and Normann came to be used as bynames and later as personal names, even among the Saxon inhabitants. The term gained a new use from 1066 onwards, when England was settled by invaders from Normandy, who were likewise of Scandinavian origin but by now largely integrated with the native population and speaking a Romance language, retaining only their original Germanic name.French : regional name for someone from Normandy.Dutch : ethnic name for a Norwegian.Jewish (Ashkenazic) : variant of Nordman.Jewish : Americanized form of some like-sounding Ashkenazic name.Swedish : from norr ‘north’ + man ‘man’.Albert Andriessen Bradt, a settler in Rensselaerswijck on the upper Hudson River in NY, was originally from Norway and was known as de Norrman (‘the Norwegian’). The waterway south of Albany which powered his mills became known as the Normanskill (‘the Norman’s Waterway’), by which name it is still known today.
Female
English
 Feminine form of English Norman, NORMA means "northman." Compare with another form of Norma.
Surname or Lastname
English
English : variant of Smith.
Boy/Male
Dutch
Smith.
Girl/Female
Latin American
Rule; pattern. Can also be a feminine form of Norman: from the North.
Boy/Male
Scottish
Smith.
Boy/Male
Dutch
Smith.
Boy/Male
Scottish
Smith.
Male
English
English form of Norwegian Normund, NORMAND means "north protection."
Girl/Female
American, Australian, British, Chinese, Christian, Danish, English, Finnish, French, German, Latin, Swedish
From the North; Pattern; Courage; Norseman; Rule; Standard; Female Version of Norman
Female
Italian
 Italian name invented by Felice Romani in his libretto for Belini's opera of the same name, derived from Latin norma, NORMA means "standard, rule." Compare with another form of Norma.
Boy/Male
English American Shakespearean
Tradesman.
Boy/Male
Arabic
Smith.
Surname or Lastname
English
English : occupational name for a worker in metal, from Middle English smith (Old English smið, probably a derivative of smītan ‘to strike, hammer’). Metal-working was one of the earliest occupations for which specialist skills were required, and its importance ensured that this term and its equivalents were perhaps the most widespread of all occupational surnames in Europe. Medieval smiths were important not only in making horseshoes, plowshares, and other domestic articles, but above all for their skill in forging swords, other weapons, and armor. This is the most frequent of all American surnames; it has also absorbed, by assimilation and translation, cognates and equivalents from many other languages (for forms, see Hanks and Hodges 1988).
Boy/Male
Dutch
Smith.
Boy/Male
Finnish
Smith.
Male
Scottish
Scottish form of Irish Gaelic Cormac, CORMAG means "son of defilement."
SMITH NORMAL-FORM
SMITH NORMAL-FORM
Boy/Male
Muslim
Fairy like flower
Boy/Male
Tamil
Elavendhan | à®à®²à®¾à®µà¯‡à®¨à¯à®¤à®¨
The honorable person in the world
Girl/Female
Hindu, Indian, Marathi
With Divine Knowledge
Surname or Lastname
English
English : variant of Stokes.
Boy/Male
Arabic, British, Hindu, Indian
Auspicious Lamp; Light
Girl/Female
Arabic, Muslim
Distinguished Sahabi RA
Boy/Male
Hindu, Indian
Pure Person; Cloud; Great
Surname or Lastname
English
English : variant of Golder.
Girl/Female
Indian, Telugu
Form the Begining
Girl/Female
Indian, Telugu
Locket
SMITH NORMAL-FORM
SMITH NORMAL-FORM
SMITH NORMAL-FORM
SMITH NORMAL-FORM
SMITH NORMAL-FORM
a.
Denoting certain hypothetical compounds, as acids from which the real acids are obtained by dehydration; thus, normal sulphuric acid and normal nitric acid are respectively S(OH)6, and N(OH)5.
n.
The workshop of a smith; a smithy or stithy.
a.
Done in due form, or with solemnity; according to regular method; not incidental, sudden or irregular; express; as, he gave his formal consent.
n.
See Wormil.
a.
Of or pertaining to Normandy or to the Normans; as, the Norman language; the Norman conquest.
a.
According to an established norm, rule, or principle; conformed to a type, standard, or regular form; performing the proper functions; not abnormal; regular; natural; analogical.
adv.
In a normal manner.
n.
The quality, state, or fact of being normal; as, the point of normalcy.
n.
See Mormal.
a.
Sound; normal.
n.
The workshop of a smith, esp. a blacksmith; a smithery; a stithy.
a.
According to a square or rule; perpendicular; forming a right angle. Specifically: Of or pertaining to a normal.
a.
Having the form or appearance without the substance or essence; external; as, formal duty; formal worship; formal courtesy, etc.
a.
Devoted to, or done in accordance with, forms or rules; punctilious; regular; orderly; methodical; of a prescribed form; exact; prim; stiff; ceremonious; as, a man formal in his dress, his gait, his conversation.
a.
Not according to rule; abnormal.
a.
Denoting that series of hydrocarbons in which no carbon atom is united with more than two other carbon atoms; as, normal pentane, hexane, etc. Cf. Iso-.