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Signal processing operation
The bilinear transform (also known as Tustin's method, after Arnold Tustin) is used in digital signal processing and discrete-time control theory to transform
Bilinear_transform
Property of many linear time-invariant (LTI) systems
domain, through the use of certain mathematical techniques such as the bilinear transform, impulse invariance, or pole–zero matching method. Thus digital IIR
Infinite_impulse_response
Linear transform from the time domain to the frequency domain
designing digital filters is to take analog designs, subject them to a bilinear transform which maps them from the s-domain to the z-domain, and then produce
Z-transform
Second order recursive digital linear filter
biquad filter can be converted into a digital design through the bilinear transform. For a filter designed in the analog s-domain, its z-domain representation
Digital_biquad_filter
discontinuity, which is why ignoring it is often safe. Bilinear transform Matched Z-transform method Jackson, L.B. (1 October 2000). "A correction to
Impulse_invariance
Karhunen–Loève transform Affine transformation (Euclidean geometry) Bäcklund transform Bilinear transform Box–Muller transform Burrows–Wheeler transform (data
List_of_transforms
Filter conversion technique
z\rightarrow -1} in much the same manner as with the bilinear transform (BLT). While this transform preserves stability and minimum phase, it preserves
Matched_Z-transform_method
Topics referred to by the same term
Look up bilinear in Wiktionary, the free dictionary. Bilinear may refer to: Bilinear sampling (also called "bilinear filtering"), a method in computer
Bilinear
Topics referred to by the same term
Bilinear transformation may refer to: Bilinear map or bilinear operator Bilinear transform (signal processing), a type of conformal map used to switch
Bilinear_transformation
Rational function of the form (az + b)/(cz + d)
to a Möbius transformation on the Riemann sphere and vice versa. Bilinear transform Conformal geometry Fuchsian group Generalised circle Hyperbolic geometry
Möbius_transformation
Discrete Fourier transform algorithm
Fourier transform (FFT) is an algorithm that computes the discrete Fourier transform (DFT), or its inverse (IDFT), of a sequence. A Fourier transform converts
Fast_Fourier_transform
Mathematical operation
is (A+iI) dom A. See self-adjoint operator for further details. Bilinear transform Extensions of symmetric operators Robert Everist Green & Steven G
Cayley_transform
Integral transform and linear operator
the Hilbert transform, such as the bilinear and trilinear Hilbert transforms are still active areas of research today. The Hilbert transform is a multiplier
Hilbert_transform
Mathematical signal manipulation by computers
the frequency response. Bilinear transform Discrete Fourier transform Discrete-time Fourier transform Fast Fourier transform Filter design Goertzel algorithm
Digital_signal_processing
Changing the resolution of a digital image
smooth edges. A common application of this can be found in pixel art. Bilinear interpolation works by interpolating pixel color values, introducing a
Image_scaling
Conversion of continuous functions into discrete counterparts
known as the bilinear transform, or Tustin transform. Each of these approximations has different stability properties. The bilinear transform preserves the
Discretization
Type of analog linear filter in electronics
group delay at ω = 0 {\displaystyle \omega =0} . Although the bilinear transform is used to convert continuous-time (analog) filters to discrete-time
Bessel_filter
Technique used in signal processing and data compression
A discrete cosine transform (DCT) expresses a finite sequence of data points in terms of a sum of cosine functions oscillating at different frequencies
Discrete_cosine_transform
Type of signal processing filter
Butterworth and other filters are often based on the bilinear transform method or the matched Z-transform method, two different methods to discretize an analog
Butterworth_filter
Australian and American mathematician (born 1975)
analogous results for the bilinear Kakeya problem which is based upon the X-ray transform instead of the Fourier transform.[TVV98] In 2003, Tao adapted
Terence_Tao
Stability criterion in control theory
How the bilinear transform maps the z-plane to the s-plane. The unstable regions for the poles of a linear control system are shaded.
Root_locus_analysis
Diagram showing the singularities of a given control system's transfer function
continuous-time or a discrete-time system: Continuous-time systems use the Laplace transform and are plotted in the s-plane: s = σ + j ω {\displaystyle s=\sigma +j\omega
Pole–zero_plot
Family of linear transformations
preserve bilinear forms of various signature. First equation in (D3) can be written more compactly as: where (·, ·) refers to the bilinear form of signature
Lorentz_transformation
quadratic nature of the transforms creates cross-terms, also called "interferences". The cross-terms caused by the bilinear structure of TFDs and TFRs
Time–frequency_representation
Overview of and topical guide to electrical engineering
Wiener filter Transforms Advanced Z-transform Bilinear transform Continuous Fourier transform Discrete cosine transform Discrete Fourier transform, Fast Fourier
Outline of electrical engineering
Outline_of_electrical_engineering
Type of analog or digital filter
recursive form via the bilinear transform. However, as digital filters have a finite bandwidth, the response shape of the transformed Chebyshev is warped
Chebyshev_filter
Device for suppressing part of a discretely-sampled signal
design and to implement and exploit nonlinear dynamics. Bessel filter Bilinear transform Butterworth filter Chebyshev filter Electronic filter Elliptical filter
Digital_filter
Matrix operation which flips a matrix over its diagonal
defines a bilinear form B : X × X → F, with the relation B(x, y) = u(x)(y). By defining the transpose of this bilinear form as the bilinear form tB defined
Transpose
Signal processing method
digital filter revolution began in the 1960s, researchers used a bilinear transform to produce infinite impulse response (IIR) digital elliptic filters
Parks–McClellan filter design algorithm
Parks–McClellan_filter_design_algorithm
Integral expressing the amount of overlap of one function as it is shifted over another
generally, Young's inequality implies that the convolution is a continuous bilinear map between suitable Lp spaces. Specifically, if 1 ≤ p, q, r ≤ ∞ satisfy:
Convolution
List of definitions of terms and concepts used in electrical engineering and electronics
control system that produces finite outputs for any finite input. bilinear transform A mathematical technique to obtain the parameters for a digital filter
Glossary of electrical and electronics engineering
Glossary_of_electrical_and_electronics_engineering
Vector space equipped with a bilinear product
field (often simply called an algebra) is a vector space equipped with a bilinear product. Thus, an algebra is an algebraic structure consisting of a set
Algebra_over_a_field
Mathematical operation on vector spaces
{\displaystyle W} (over the same field) is a vector space to which is associated a bilinear map V × W → V ⊗ W {\displaystyle V\times W\rightarrow V\otimes W} that
Tensor_product
Part of signal analysis and signal processing
utilizes bilinear transformations. Compared with other time–frequency analysis techniques, such as short-time Fourier transform (STFT), the bilinear-transformation
Bilinear time–frequency distribution
Bilinear_time–frequency_distribution
Mathematical description of spacetime used in relativity
the polarization identity the quadratic form is converted to a symmetric bilinear form called the Minkowski inner product, though it is not a geometric inner
Minkowski_spacetime
Generalization of the discrete Fourier transform
Fourier transform on finite groups is a generalization of the discrete Fourier transform from cyclic to arbitrary finite groups. The Fourier transform of a
Fourier transform on finite groups
Fourier_transform_on_finite_groups
Structure defining distance on a manifold
a metric tensor at a point p of M is a bilinear form defined on the tangent space at p (that is, a bilinear function that maps pairs of tangent vectors
Metric_tensor
Auditory frequency metric
to Bark scale at Wikimedia Commons Smith and Abel – Bark and ERB Bilinear Transforms (1999) Archived 2008-03-25 at the Wayback Machine Auditory scales
Bark_scale
Coordinate change in linear algebra
the bilinear form on the "new" basis is Φ ′ = P T Φ P . {\displaystyle \mathbf {\Phi '} =P^{\mathsf {T}}\mathbf {\Phi } P.} A symmetric bilinear form
Change_of_basis
Measure used in psychoacoustics
(10 May 2007). "Equivalent Rectangular Bandwidth". Bark and ERB Bilinear Transforms. Center for Computer Research in Music and Acoustics (CCRMA), Stanford
Equivalent rectangular bandwidth
Equivalent_rectangular_bandwidth
Group of rotations in 3 dimensions
g θ , {\displaystyle g_{\phi },g_{\theta },} thus correspond to bilinear transforms of R2 ≃ C ≃ M, namely, they are examples of Möbius transformations
3D_rotation_group
Topics referred to by the same term
Unified School District Tustin's method, an alternate name for the bilinear transform, a digital-control approximation This disambiguation page lists articles
Tustin_(disambiguation)
Relativistic quantum mechanical wave equation
spinor is useful in forming Lorentz invariant quantities. For example, the bilinear ψ † ψ {\displaystyle \psi ^{\dagger }\psi } is not Lorentz invariant, but
Dirac_equation
General concept and operation in mathematics
mathematical dualities between objects of two types correspond to pairings, bilinear functions from an object of one type and another object of the second type
Duality_(mathematics)
Generalization of perpendicularity
of perpendicularity to linear algebra of bilinear forms. Two elements u and v of a vector space with bilinear form B {\displaystyle B} are orthogonal when
Orthogonality_(mathematics)
Method for solving continuous operator problems (such as differential equations)
(after Walther Ritz) typically assumes symmetric and positive-definite bilinear form in the weak formulation, where the differential equation for a physical
Galerkin_method
The symmetrization and antisymmetrization of a bilinear map are bilinear; thus away from 2, every bilinear form is a sum of a symmetric form and a skew-symmetric
Symmetrization
Polynomial with all terms of degree two
{T}}Ay=y^{\mathsf {T}}Ax.} Thus, bq is a symmetric bilinear form over K with matrix A. Conversely, any symmetric bilinear form b defines a quadratic form q ( x )
Quadratic_form
Signal processing algorithm
the distribution of energy in multi-component signals. Cohen's class of bilinear time-frequency representations is a class of "smoothed" Wigner–Ville distributions
Reassignment_method
German mathematician
Bonn. He is famous for work (joint with Michael Lacey) on the bilinear Hilbert transform and for giving a simplified proof of Carleson's theorem; the techniques
Christoph_Thiele
Theorem
distributions) have a two-variable theory that includes all reasonable bilinear forms on the space D {\displaystyle {\mathcal {D}}} of test functions.
Schwartz_kernel_theorem
| T | {\displaystyle T=U|T|} is its polar decomposition, the Aluthge transform of T {\displaystyle T} is the operator Δ ( T ) {\displaystyle \Delta (T)}
Aluthge_transform
Mathematical concept
In mathematics, the seven-dimensional cross product is a bilinear operation on vectors in seven-dimensional Euclidean space. It assigns to any two vectors
Seven-dimensional cross product
Seven-dimensional_cross_product
Space in mathematics and theoretical physics
terms of the bilinear form: q(x) = ⟨x, x⟩. When ⟨x, y⟩ = 0, x and y are orthogonal vectors of the pseudo-Euclidean space. This bilinear form is often
Pseudo-Euclidean_space
Beckman Instruments Bell Telephone Laboratories Biasing BIBO stability Bilinear transform Bimetallic strip Biofuel Biomass Biomedical engineering Biot–Savart
Index of electrical engineering articles
Index_of_electrical_engineering_articles
Type of group in mathematics
{T}}Q=QQ^{\mathsf {T}}=I\right\}.} More generally, given a non-degenerate symmetric bilinear form or quadratic form on a vector space over a field, the orthogonal group
Orthogonal_group
Type of function
is a vector space equipped with a bilinear form. When the function space has an interval as the domain, the bilinear form may be the integral of the product
Orthogonal_functions
Method for estimating new data within known data points
integration path, regardless of the length of the integration path. Linear, bilinear and trilinear interpolation are also considered mimetic, even if it is
Interpolation
Property of certain dynamical systems
which involved replacing the original nonlinear dynamical system with a bilinear system of constant coefficient equations for an auxiliary quantity, which
Integrable_system
Type of polynomial
interpolation on a rectangular grid, a generalization of linear interpolation, bilinear interpolation and trilinear interpolation to an arbitrary number of variables
Multilinear_polynomial
Video compression format, succeeds H.264/MPEG-4 AVC
integer discrete cosine transform (DCT) with 4×4 and 8×8 block sizes, HEVC uses both integer DCT and discrete sine transform (DST) with varied block sizes
High_Efficiency_Video_Coding
Central object of study in category theory
finite-dimensional vector spaces with a nondegenerate bilinear form, and maps linear transforms that respect the bilinear form, by construction has a natural isomorphism
Natural_transformation
Signal processing
useful and popular methods form a class referred to as "quadratic" or bilinear time–frequency distributions. A core member of this class is the Wigner–Ville
Transformation between distributions in time–frequency analysis
Transformation_between_distributions_in_time–frequency_analysis
Lossy compression method for reducing the size of digital images
Experts Group created the standard in 1992, based on the discrete cosine transform (DCT) algorithm. JPEG was largely responsible for the proliferation of
JPEG
Part of signal processing in time-frequency analysis
Wigner distribution function (WDF) is used in signal processing as a transform in time-frequency analysis. The WDF was first proposed in physics to account
Wigner_distribution_function
Vector space with generalized dot product
sesquilinearity reduces to bilinearity. Hence an inner product on a real vector space is a positive-definite symmetric bilinear form. The binomial expansion
Inner_product_space
Vector behavior under coordinate changes
finite-dimensional vector space V over a field K with a non-degenerate symmetric bilinear form g : V × V → K (which may be referred to as the metric tensor), there
Covariance and contravariance of vectors
Covariance_and_contravariance_of_vectors
Techniques and methods in signal processing
distributions, such as: Short-time Fourier transform (including the Gabor transform), Wavelet transform, Bilinear time–frequency distribution function (Wigner
Time–frequency_analysis
Area of mathematical analysis
restriction theorem for the sphere. More advanced restriction problems involve bilinear and multilinear estimates, wave-packet decompositions, induction on scales
Harmonic_analysis
American mathematician
the tenure of this fellowship he began a study of the bilinear Hilbert transform. This transform was at the time the subject of a conjecture by Alberto
Michael_Lacey_(mathematician)
Theorem on operator interpolation
Riesz (1927). The proof makes use of convexity results in the theory of bilinear forms. For this reason, many classical references such as Stein and Weiss
Riesz–Thorin_theorem
Algebraic object with geometric applications
indices, and n + m gives the total order of the tensor. For example, a bilinear form is the same thing as a (0, 2)-tensor; an inner product is an example
Tensor
Mathematical description of fermions
the matrix into the usual power series for the exponential function. A bilinear form of Dirac spinors can be reduced to five irreducible (under the Lorentz
Dirac_spinor
Space of complex matrices with positive definite imaginary part
_{a_{j}}\omega _{i}\ ,\ \int _{b_{j}}\omega _{i}\right).} The Riemann bilinear relations imply that the g × g {\displaystyle g\times g} matrix of a {\displaystyle
Siegel_upper_half-space
An anamorphic stretch transform (AST) also referred to as warped stretch transform is a physics-inspired signal transform that emerged from time stretch
Anamorphic_stretch_transform
Computational hardness assumption
with a pairing e : G × G → T {\displaystyle e:G\times G\to T} which is bilinear. This map gives an efficient algorithm to solve the decisional Diffie-Hellman
Decision_Linear_assumption
Algebra based on a vector space with a quadratic form
v\rangle ={\frac {1}{2}}\left(Q(u+v)-Q(u)-Q(v)\right)} is the symmetric bilinear form associated with Q, via the polarization identity. Quadratic forms
Clifford_algebra
Broad concept generalizing scalars in mathematics and physics
space, a vector space V equipped with a non-degenerate, skew-symmetric, bilinear form Topological vector space, a blend of topological structure with the
Vector (mathematics and physics)
Vector_(mathematics_and_physics)
Model in digital signal processing
function H(s) = (1+sT)/(sT). Nyquist–Shannon sampling theorem Zero-order hold Bilinear interpolation Sankar, Krishna (2007). "Zero order hold and first order
First-order_hold
Physics concept
,\mathbf {u} \rangle } is a real number. This notation emphasizes the bilinear character of the form. It is linear in σ since that is a linear function
Covariant_transformation
Real numbers adjoined with a nil-squaring element
follows from the property ε2 = 0 and the fact that multiplication is a bilinear operation. The dual numbers form a commutative algebra of dimension two
Dual_number
In functional analysis, a Hilbert space
F(\omega )=\int _{-\infty }^{\infty }f(t)e^{-i\omega t}\,dt} is the Fourier transform of f {\displaystyle f} . As the inner product, we use ⟨ f , g ⟩ L 2 =
Reproducing kernel Hilbert space
Reproducing_kernel_Hilbert_space
Identities involving spinor bilinears
identity that allows one to rewrite bilinears of the product of two spinors as a linear combination of products of the bilinears of the individual spinors. It
Fierz_identity
Public-key cryptographic pseudorandom function
g)^{1/(x+SK)}\quad {\mbox{and}}\quad p_{SK}(x)=g^{1/(x+SK)},} where e(·,·) is a bilinear map. To verify whether F S K ( x ) {\displaystyle F_{SK}(x)} was computed
Verifiable_random_function
Video compression technique, used to efficiently predict and generate video frames
and full-samples, the sub-samples can be calculated by using bicubic or bilinear 2-D filtering. See subclause 8.4.2.2 "Fractional sample interpolation process"
Motion_compensation
Optical imaging technique
method the tradeoff is this between time and frequency resolutions. Bilinear transforms may be applied, where under the right conditions have a reduced resolution
Spectroscopic optical coherence tomography
Spectroscopic_optical_coherence_tomography
Mathematical operation in quantum optics, general relativity and other areas of physics
Bogoliubov transform becomes obvious is that in mean-field approximation the Hamiltonian of the system can be written in both cases as a sum of bilinear terms
Bogoliubov_transformation
generated by the polarizability tensor. Since tensor components transform as bilinear products of two spatial coordinates, they are invariant under inversion
Rule_of_mutual_exclusion
Covariance and correlation
affine transform. Specifically, T i ( ⋅ ) {\displaystyle T_{i}(\cdot )} can be circular translation transform, rotation transform, or scale transform, etc
Cross-correlation
Notions of sums for matrices in linear algebra
transformation separately onto v → {\displaystyle {\vec {v}}\!} , then adding the transformed vectors. A v → + B v → = ( A + B ) v → {\displaystyle \mathbf {A} {\vec
Matrix_addition
Memory-saving rendering technique in which resolution of farther-away images is lowered
limited number of texture samples per display pixel (as is the case with bilinear filtering) then artifacts are reduced since the mipmap images are effectively
Mipmap
Non-tensorial representation of the spin group
a finite-dimensional complex vector space with nondegenerate symmetric bilinear form g. The Clifford algebra Cℓ(V, g) is the algebra generated by V subject
Spinor
Orthogonal group of an indefinite quadratic form
-dimensional real vector space that leave invariant a nondegenerate, symmetric bilinear form of signature ( p , q ) {\displaystyle (p,q)} , where n = p + q {\displaystyle
Indefinite_orthogonal_group
Type of random variable ordering
6\times 30+0.4\times 20\succeq _{\mathrm {dd} }0.5\times 20+0.5\times 10} . Bilinear dominance, denoted A ⪰ b d B {\displaystyle A\succeq _{\mathrm {bd} }B}
Stochastic_ordering
Method of enhancing the image quality of textures on surfaces of computer graphics
amounts of filtering in different directions, unlike simpler methods like bilinear and trilinear filtering which filter equally in all directions. While it
Anisotropic_filtering
Cryptographic primitive
precisely, the proof in such proof systems consists only of a small number of bilinear group elements. Gong, Yinjie; Jin, Yifei; Li, Yuchan; Liu, Ziyi; Zhu, Zhiyi
Non-interactive zero-knowledge proof
Non-interactive_zero-knowledge_proof
Mathematical operation on vectors in 3D space
\mathbf {b} .} The product rule of differential calculus applies to any bilinear operation, and therefore also to the cross product: d d t ( a × b ) = d
Cross_product
Operator that involves integration
operators, which are linear operators induced by bilinear forms involving integrals Integral transforms, which are maps between two function spaces, which
Integral_operator
Topological vector spaces
}(U)\to C_{\text{c}}^{\infty }(U)} is a continuous linear operator. The bilinear multiplication map C ∞ ( R m ) × C c ∞ ( R n ) → C c ∞ ( R m + n ) {\displaystyle
Spaces of test functions and distributions
Spaces_of_test_functions_and_distributions
Form of a matrix
cross product a × b {\displaystyle \mathbf {a} \times \mathbf {b} } is a bilinear map, which means that by fixing one of the two arguments, for example a
Skew-symmetric_matrix
BILINEAR TRANSFORM
BILINEAR TRANSFORM
Surname or Lastname
English
English : habitational name from Lichfield in Staffordshire. The first element preserves a British name recorded as Letocetum during the Romano-British period. This means ‘gray wood’, from words which are the ancestors of Welsh llŵyd ‘gray’ and coed ‘wood’. By the Old English period this had been reduced to Licced, and the element feld ‘pasture’, ‘open country’ was added to describe a patch of cleared land within the ancient wood.English : habitational name from Litchfield in Hampshire, recorded in Domesday Book as Liveselle. This is probably from an Old English hlīf ‘shelter’ + Old English scylf ‘shelf’, ‘ledge’. The subsequent transformation of the place name may be the result of folk etymological association with Old English hlið, hlid ‘slope’ + feld ‘open country’.
Girl/Female
Greek
Bee. Famous bearer: Melissa, Mythological princess of Crete transformed to a bee after learning...
Girl/Female
Greek
Most beautiful. In Mythology the Arcadian nymph Calista transformed into a she-bear; then into...
Girl/Female
Greek American
Bee. Famous bearer: Melissa, Mythological princess of Crete transformed to a bee after learning...
Boy/Male
Hindu, Indian, Punjabi, Sikh
The Brave God
Surname or Lastname
Scottish
Scottish : nickname for someone with streaks of gray or white hair, from Gaelic riabhach ‘brindled’, ‘grayish’.English : habitational name from either of two places called Reach, in Bedfordshire and Cambridgeshire, from Old English rǣc ‘raised strip of land or other linear feature’ (in the case of the Cambridgeshire name referring to Devil’s Dyke, a post-Roman earthwork).
Girl/Female
Latin
or Selena. One of seven mythological daughters of Atlas transformed by Zeus into stars of the...
Girl/Female
Arabic
Pomegranate Flower
Girl/Female
Greek
Bee. Famous bearer: Melissa, Mythological princess of Crete transformed to a bee after learning...
Girl/Female
Greek
Bee. Famous bearer: Melissa, Mythological princess of Crete transformed to a bee after learning...
Girl/Female
Latin
or Selena. One of seven mythological daughters of Atlas transformed by Zeus into stars of the...
Girl/Female
Latin
or Selena. One of seven mythological daughters of Atlas transformed by Zeus into stars of the...
Girl/Female
Greek
The laurel tree. The mythological virtuous Daphne was transformed into a laurel tree to protect...
Girl/Female
Israeli
The laurel tree. The mythological virtuous Daphne was transformed into a laurel tree to protect...
Girl/Female
Greek
Bee. Famous bearer: Melissa, Mythological princess of Crete transformed to a bee after learning...
Girl/Female
Greek
Most beautiful. Calista was a Mythological Arcadian who transformed into a she-bear, then into...
Girl/Female
Greek Latin
Most beautiful. Calista was a Mythological Arcadian who transformed into a she-bear, then into...
Girl/Female
Greek American
Bee. Famous bearer: Melissa, Mythological princess of Crete transformed to a bee after learning...
Surname or Lastname
English
English : variant of Pillar 1–3.German : variant of Pille (from Bilihar, composed of bil ‘sword’ + hari ‘army’).Jewish (Ashkenazic) : unexplained.
Surname or Lastname
English and French
English and French : regional name from Old French Poitevin, denoting someone from Poitou in western France. The form Potvin has long been established in England and was brought to the U.S. from there. However, French bearers of the surname Poitevin also came to the New World, where their surname underwent a similar transformation on arrival in New England.
BILINEAR TRANSFORM
BILINEAR TRANSFORM
Female
Swiss
, addition.
Boy/Male
Tamil
Gold
Boy/Male
Polish Czechoslovakian
God is gracious.
Male
German
German byname for "a hunter of badgers" or someone who "has badger-like qualities," derived from the vocabulary word dahs, DACHS means "badger."Â
Girl/Female
Tamil
Jolly, Happy
Male
Babylonian
, an official scribe in the reign of Gamilsin.
Boy/Male
Indian, Punjabi, Sikh
Earning the Wealth of Naam
Girl/Female
Hindu
Decorated, Adorned
Boy/Male
Indian
Continuous; Without Break
Girl/Female
Anglo Saxon
Bears children.
BILINEAR TRANSFORM
BILINEAR TRANSFORM
BILINEAR TRANSFORM
BILINEAR TRANSFORM
BILINEAR TRANSFORM
a.
Linear.
n.
A European perennial herb (Asperula cynanchica) with narrowly linear whorled leaves; -- formerly thought to cure the quinsy. Also called quincewort.
a.
Very narrow, and tapering gradually to a fine point from a broadish base; awl-shaped; linear.
a.
Of, pertaining to, or included by, three lines; as, trilinear coordinates.
a.
Shaped like a tongue; specifically (Bot.), linear or oblong, and fleshy, blunt at the end, and convex beneath; as, a tongue-shaped leaf.
a.
Of a linear shape.
adv.
In a linear manner; with lines.
a.
Of or pertaining to a line; consisting of lines; in a straight direction; lineal.
a.
Having many segments; cleft into several parts by linear sinuses; as, a multifid leaf or corolla.
a.
A drawing in linear perspective.
a.
In the direction of a line; of or pertaining to a line; measured on, or ascertained by, a line; linear; as, lineal magnitude.
n.
A painted tape, marked with linear dimensions, as inches, feet, etc., and often inclosed in a case, -- used for measuring.
superl.
Not long; having brief length or linear extension; as, a short distance; a short piece of timber; a short flight.
a.
Of, pertaining to, or included by, two lines; as, bilinear coordinates.
a.
Like a line; narrow; of the same breadth throughout, except at the extremities; as, a linear leaf.
n.
An invariable quantity; specifically, a function of the coefficients of one or more forms, which remains unaltered, when these undergo suitable linear transformations.
a.
Cleft to the middle or slightly beyond the middle; opening with a cleft; divided by a linear sinus, with straight margins.
a.
Shaped like spatula, or like a battledoor, being roundish, with a long, narrow, linear base.
a.
See Bilingual.
n.
A linear apothecium furrowed along the middle; the fruit of certain lichens.