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Matrix whose entries are all 0
mathematics, particularly linear algebra, a zero matrix or null matrix is a matrix all of whose entries are zero. It also serves as the additive identity
Zero_matrix
Matrix in which most of the elements are zero
sparse matrix or sparse array is a matrix in which most of the elements are zero. There is no strict definition regarding the proportion of zero-value
Sparse_matrix
Array of numbers
maps involving the zero vector space. For example, if A is a 3 × 0 matrix and B is a 0 × 3 matrix, then AB is the 3 × 3 zero matrix corresponding to the
Matrix_(mathematics)
Square matrix with ones on the main diagonal and zeros elsewhere
the identity matrix of size n {\displaystyle n} is the n × n {\displaystyle n\times n} square matrix with ones on the main diagonal and zeros elsewhere.
Identity_matrix
Matrix whose only nonzero elements are on its main diagonal
In linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero; the term usually refers to square matrices
Diagonal_matrix
Square matrix used to represent a graph or network
adjacency matrix is a (0,1)-matrix with zeros on its diagonal. If the graph is undirected (i.e. all of its edges are bidirectional), the adjacency matrix is
Adjacency_matrix
Norm on a vector space of matrices
such norms are referred to as matrix norms. Matrix norms behave in certain ways like the distance from the zero matrix. They are distinguished from the
Matrix_norm
Generalizations of '"`UNIQ--math-00000000-QINU`"' in algebraic structures
to the zero matrix. In a matrix ring, the zero matrix serves the role of both an additive identity and an absorbing element. In general, the zero element
Zero_element
For a square matrix, the transpose of the cofactor matrix
a real matrix is the transpose. The product of a matrix with its adjugate gives a diagonal matrix (entries not on the main diagonal are zero) whose diagonal
Adjugate_matrix
Matrix that converges to zero matrix
algebra, a convergent matrix is a matrix that converges to the zero matrix under matrix exponentiation. When successive powers of a matrix T become small (that
Convergent_matrix
Dimension of the column space of a matrix
\end{aligned}}} The final matrix (in reduced row echelon form) has two non-zero rows and thus the rank of matrix A is 2. When applied to floating
Rank_(linear_algebra)
Special kind of square matrix
triangular matrix is a special kind of square matrix. A square matrix is called lower triangular if all the entries above the main diagonal are zero. Similarly
Triangular_matrix
Property of a mathematical matrix
to be positive or zero (that is, nonnegative). Negative-definite and negative semi-definite matrices are defined analogously. A matrix that is not positive
Definite_matrix
Matrix with a multiplicative inverse
For a real matrix, this is reflected by its determinant: an invertible matrix has nonzero determinant, while a matrix with determinant zero collapses volume
Invertible_matrix
Matrix representation of a graph
theory, the Laplacian matrix, also called the graph Laplacian, admittance matrix, Kirchhoff matrix, or discrete Laplacian, is a matrix representation of a
Laplacian_matrix
a 2×2 matrix M is another 2×2 matrix R such that M = R2, where R2 stands for the matrix product of R with itself. In general, there can be zero, two,
Square root of a 2 by 2 matrix
Square_root_of_a_2_by_2_matrix
Matrix whose entries are integers
integer matrix is a matrix whose entries are all integers. Examples include binary matrices, the zero matrix, the matrix of ones, the identity matrix, and
Integer_matrix
1998 video game
Matrix Zero was released August 30, 2002 for the Game Boy Advance. Black Matrix Zero is set in the same fictional world as the original Black/Matrix game
Black/Matrix
Most widely known generalized inverse of a matrix
A^{+}} of a matrix A {\displaystyle A} , often called the pseudoinverse, is the most widely known generalization of the inverse matrix. It was independently
Moore–Penrose_inverse
Square matrix without an inverse
Ax=0} admits non-zero solutions. These characterizations follow from standard rank-nullity and invertibility theorems: for a square matrix A, det ( A ) ≠
Singular_matrix
Matrix with non-zero elements only in a diagonal band
In mathematics, particularly matrix theory, a band matrix or banded matrix is a sparse matrix whose non-zero entries are confined to a diagonal band,
Band_matrix
&0\\\vdots &\vdots &\ddots &\vdots \\0&0&\cdots &1\end{bmatrix}}.} and the zero matrix of dimension m × n {\displaystyle m\times n} . For example: O 2 × 3 =
List_of_named_matrices
Matrix of partial derivatives of a vector-valued function
vector calculus, the Jacobian matrix (/dʒəˈkoʊbiən/, /dʒɪ-, jɪ-/) of a vector-valued function of several variables is the matrix of all its first-order partial
Jacobian matrix and determinant
Jacobian_matrix_and_determinant
Square matrix with ones on a superdiagonal or subdiagonal
mathematics, a shift matrix is a binary matrix with ones only on the superdiagonal or subdiagonal, and zeroes elsewhere. A shift matrix U with ones on the
Shift_matrix
Topics referred to by the same term
for zero manifold Several terms related to 0 (number) Zero map, see constant function Zero morphism, a kind of morphism in category theory Zero matrix, a
0M
Matrix with the same number of rows and columns
mathematics, a square matrix is a matrix with the same number of rows and columns. An n-by-n matrix is known as a square matrix of order n {\displaystyle
Square_matrix
Matrix that commutes with its conjugate transpose
number. In particular, the zero matrix is analogous to 0, and the identity matrix is analogous to 1. An idempotent matrix is an orthogonal projection
Normal_matrix
Matrix representing a Euclidean rotation
rotation matrix is a transformation matrix that is used to perform a rotation in Euclidean space. For example, using the convention below, the matrix R = [
Rotation_matrix
Polynomial whose roots are the eigenvalues of a matrix
polynomial to zero. In spectral graph theory, the characteristic polynomial of a graph is the characteristic polynomial of its adjacency matrix. Eigenvalues
Characteristic_polynomial
Mathematical ring whose elements are matrices
abstract algebra, a matrix ring is a set of matrices with entries in a ring R that form a ring under matrix addition and matrix multiplication. The set
Matrix_ring
In mathematics, invariant of square matrices
corresponding linear map is an isomorphism. However, if the determinant is zero, the matrix is referred to as singular, meaning it does not have an inverse. The
Determinant
Matrix of binary truth values
matrix, binary matrix, relation matrix, Boolean matrix, or (0, 1)-matrix is a matrix with entries from the Boolean domain B = {0, 1}. Such a matrix can
Logical_matrix
Real numbers adjoined with a nil-squaring element
the zero matrix, corresponding to the dual number ε {\displaystyle \varepsilon } . Generally, if ε {\displaystyle \varepsilon } is a nilpotent matrix, then
Dual_number
Type of square matrix
probability and combinatorics, a doubly stochastic matrix (also called bistochastic matrix) is a square matrix X = ( x i j ) {\displaystyle X=(x_{ij})} of nonnegative
Doubly_stochastic_matrix
Matrix equal to its conjugate-transpose
In mathematics, a Hermitian matrix (or self-adjoint matrix) is a square matrix with complex-valued entries that is equal to its own conjugate transpose
Hermitian_matrix
Matrix of second derivatives
In mathematics, the Hessian matrix, Hessian or (less commonly) Hesse matrix is a square matrix of second-order partial derivatives of a scalar-valued function
Hessian_matrix
Branch of mathematics
correspond to change of bases in W. Every matrix is similar to an identity matrix possibly bordered by zero rows and zero columns. In terms of vector spaces
Linear_algebra
integer coefficients, whether the zero matrix can be expressed as a finite product of matrices from this set. The matrix mortality problem is known to be
Matrix_mortality_problem
Matrix with every entry equal to one
dimensions. Zero matrix, a matrix where all entries are zero Single-entry matrix Horn, Roger A.; Johnson, Charles R. (2012), "0.2.8 The all-ones matrix and vector"
Matrix_of_ones
Situation where total gains match total losses
for a two-player, zero-sum game can be found by solving a linear programming problem. Suppose a zero-sum game has a payoff matrix M where element Mi
Zero-sum_game
Theorem in linear algebra
example of a primitive matrix with zero diagonal. If the diagonal of an irreducible non-negative square matrix is non-zero then the matrix must be primitive
Perron–Frobenius_theorem
Matrix equal to its transpose
element of a skew-symmetric matrix must be zero, since each is its own negative. In linear algebra, a real symmetric matrix represents a self-adjoint operator
Symmetric_matrix
Kind of square matrix in linear algebra
a Hessenberg matrix is a special kind of square matrix, one that is "almost" triangular. To be exact, an upper Hessenberg matrix has zero entries below
Hessenberg_matrix
Matrix decomposition
{\Sigma } _{r}} is an r × r {\displaystyle r\times r} matrix with only the non-zero singular values (allowing repetitions) on its main diagonal
Singular_value_decomposition
Square matrices satisfy their characteristic equation
Cayley–Hamilton theorem states that this polynomial expression is equal to the zero matrix, which is to say that p A ( A ) = 0 ; {\displaystyle p_{A}(A)=0;} that
Cayley–Hamilton_theorem
Matrix decomposition
} where R1 is an n×n upper triangular matrix, 0 is an (m − n)×n zero matrix, Q1 is m×n, Q2 is m×(m − n), and Q1 and Q2 both have orthogonal
QR_decomposition
Real square matrix whose columns and rows are orthogonal unit vectors
In linear algebra, an orthogonal matrix or orthonormal matrix Q, is a real-valued square matrix whose columns and rows are orthonormal vectors. One way
Orthogonal_matrix
Mathematical term
} For the zero matrix and the identity matrix, the spread is zero. The zero matrix has only zero as its eigenvalues, and the identity matrix has only one
Spread_of_a_matrix
Two-dimensional matrix barcode
A Data Matrix is a two-dimensional code consisting of black and white "cells" or dots arranged in either a square or rectangular pattern, also known as
Data_Matrix
Mathematical operation on invertible matrices
mathematics, a logarithm of a matrix is another matrix such that the matrix exponential of the latter matrix equals the original matrix. It is thus a generalization
Logarithm_of_a_matrix
Mathematical operation in linear algebra
columns in the first matrix must be equal to the number of rows in the second matrix. The resulting matrix, known as the matrix product, has the number
Matrix_multiplication
Mathematical concept in algebra
triangular matrix with zeros along the main diagonal is nilpotent, with index ≤ n {\displaystyle \leq n} [citation needed]. For example, the matrix B = [ 0
Nilpotent_matrix
Matrix of geometric progressions
all zero-based indices i {\displaystyle i} and j {\displaystyle j} . Some authors define the Vandermonde matrix as the transpose of the above matrix. The
Vandermonde_matrix
Matrix of inner products of vectors
if and only if the Gram determinant (the determinant of the Gram matrix) is non-zero. It is named after Jørgen Pedersen Gram. For finite-dimensional real
Gram_matrix
Measure of covariance of components of a random vector
covariance matrix (also known as auto-covariance matrix, dispersion matrix, variance matrix, or variance–covariance matrix) is a square matrix giving the
Covariance_matrix
Specific element of an algebraic structure
orthogonal to any element multiplied. That is, it is not possible to obtain a non-zero vector in the same direction as the original. Yet another example of structure
Identity_element
Markov chain in which all states can be absorbing
&I_{r}\end{bmatrix}},} where Q is a t-by-t matrix, R is a nonzero t-by-r matrix, 0 is an r-by-t zero matrix, and Ir is the r-by-r identity matrix. Thus, Q describes the probability
Absorbing_Markov_chain
Concept in linear algebra
the n × n {\displaystyle n\times n} zero matrix over K {\displaystyle K} . A particular case is a linear matrix pencil L ( λ ) = A − λ B {\displaystyle
Matrix_pencil
1986 book by William Gibson
program counter to zero when powered on or reset. In Count Zero Gibson presents "a high-tech near-future of linked super-computers... [a matrix that] has given
Count_Zero
Sum of elements on the main diagonal
square matrix with zero trace is unitarily equivalent to a square matrix with diagonal consisting of all zeros. The trace of the n × n identity matrix is
Trace_(linear_algebra)
Several types of mathematical matrix containing zeroes
a hollow matrix may refer to one of several related classes of matrix: a sparse matrix; a matrix with a large block of zeroes; or a matrix with diagonal
Hollow_matrix
Type of matrix in probability theory and statistics
{\displaystyle 0_{p\times q}} is a p × q {\displaystyle p\times q} matrix of zeroes. If Z {\displaystyle \mathbf {Z} } and W {\displaystyle \mathbf {W}
Cross-covariance_matrix
Computer vision geometry concept
camera matrix and the ∼ {\displaystyle \,\sim } sign implies that the left and right hand sides are equal except for a multiplication by a non-zero scalar
Camera_matrix
Vectors mapped to 0 by a linear map
contains the zero vector, since A0 = 0. If x ∈ Null(A) and y ∈ Null(A), then x + y ∈ Null(A). This follows from the distributivity of matrix multiplication
Kernel_(linear_algebra)
Polynomial with a matrix as variable
polynomial is viewed as a matrix polynomial and evaluated at the matrix A {\displaystyle A} itself, the result is the zero matrix: p A ( A ) = 0 {\displaystyle
Matrix_polynomial
Matrix decomposition
(also known as eigenvalue decomposition or EVD) is a factorization of a matrix A {\displaystyle A} into a canonical form given by A = V D V T {\displaystyle
Eigendecomposition of a matrix
Eigendecomposition_of_a_matrix
Matrix operation generalizing exponentiation of scalar numbers
arbitrary complex numbers. We denote the n × n identity matrix by I and the zero matrix by 0. The matrix exponential satisfies the following properties. We
Matrix_exponential
In linear algebra, the inverse square matrix A {\displaystyle A} is another square matrix A − 1 {\displaystyle A^{-1}} such that the product A − 1 A {\displaystyle
Methods_of_matrix_inversion
Stochastic matrix representing links between entities
A Google matrix is a particular stochastic matrix that is used by Google's PageRank algorithm. The matrix represents a graph with edges representing links
Google_matrix
Topics referred to by the same term
(triple letter "O") Zero point (disambiguation) Point of origin (disambiguation) Black (0, 0, 0) in RBG color model Zero matrix This disambiguation page
Triple_zero
Matrix in linear algebra
positive-semidefinite matrix is copositive by definition. Every symmetric nonnegative matrix is copositive. This includes the zero matrix. The exchange matrix ( 0 1 1
Copositive_matrix
Matrix with no negative elements
nonnegative matrix, written X ≥ 0 , {\displaystyle \mathbf {X} \geq 0,} is a matrix in which all the elements are equal to or greater than zero, that is
Nonnegative_matrix
Relation of a matrix of variables between two points in time
This solution motivates the above stability result: At shrinks to the zero matrix over time if and only if the eigenvalues of A are all less than unity
Matrix_difference_equation
Matrix defined using smaller matrices called blocks
In mathematics, a block matrix or a partitioned matrix is a matrix that is interpreted as having been broken into sections called blocks or submatrices
Block_matrix
Concept in linear algebra
x i-1 square upper triangular matrix, 0 represents the n-i+1 x n-i+1 zero matrix, * represents an n-i+1 x n-i+1 matrix, and P v {\displaystyle P_{v}}
Householder_transformation
Algorithm for solving systems of linear equations
elementary row operations to modify the matrix until the lower left-hand corner of the matrix is filled with zeros, as much as possible. There are three
Gaussian_elimination
Random process independent of past history
identity matrix of size n, and 0n,n is the zero matrix of size n×n. Multiplying together stochastic matrices always yields another stochastic matrix, so Q
Markov_chain
Approximation of a matrix's Cholesky factorization
decomposition, we observe that some zero elements in the original matrix end up being non-zero elements in the decomposed matrix, like elements (4,2), (5,2) and
Incomplete Cholesky factorization
Incomplete_Cholesky_factorization
Spectral line splitting in electrical field
element of the Wigner D-matrix. The first-order perturbation matrix on basis of the unperturbed rigid rotor function is non-zero and can be diagonalized
Stark_effect
Form of a matrix indicating its eigenvalues and their algebraic multiplicities
{red}\lrcorner }\\\end{array}}\right]} Example of a matrix in Jordan normal form. All matrix entries not shown are zero. The outlined squares are known as "Jordan
Jordan_normal_form
Table layout for visualizing performance; also called an error matrix
A confusion matrix, also known as error matrix, is a specific table layout that allows visualization of the performance of a person or an algorithm on
Confusion_matrix
Mathematical model of a system in control engineering
feedforward) matrix" (in cases where the system model does not have a direct feedthrough, D ( ⋅ ) {\displaystyle \mathbf {D} (\cdot )} is the zero matrix), dim
State-space_representation
Matrix of values of explanatory variables
The design matrix is used in certain statistical models, e.g., the general linear model. It can contain indicator variables (ones and zeros) that indicate
Design_matrix
In mathematics, a bidiagonal matrix is a banded matrix with non-zero entries along the main diagonal and either the diagonal above or the diagonal below
Bidiagonal_matrix
Possible form of a matrix
rank of the entire matrix, X is a matrix with j {\displaystyle j} rows and n − j {\displaystyle n-j} columns, and the two 0's are zero matrices of appropriate
Row_echelon_form
Value that makes no change when added
matrices over a ring R, the additive identity is the zero matrix, denoted O or 0, and is the m-by-n matrix whose entries consist entirely of the identity element
Additive_identity
Concepts from linear algebra
of these vectors. A matrix whose elements above the main diagonal are all zero is called a lower triangular matrix, while a matrix whose elements below
Eigenvalues_and_eigenvectors
Block diagonal matrix of Jordan blocks
discipline of matrix theory, a Jordan matrix, named after Camille Jordan, is a block diagonal matrix over a ring R (whose identities are the zero (0) and one
Jordan_matrix
Form of a matrix
diagonal elements of a skew-symmetric matrix are zeros because each element must be its own negative. The matrix A = [ 0 2 − 45 − 2 0 − 4 45 4 0 ] {\displaystyle
Skew-symmetric_matrix
2003 American-Japanese-South Korean anthology anime film
includes nine animated short films, some of which provide backstory for The Matrix film series, while others present side stories. The Animatrix was released
The_Animatrix
Used for the resultant of two polynomials
polynomials. The determinant of the Sylvester matrix of two polynomials is their resultant, which is zero when the two polynomials have a common root (in
Sylvester_matrix
Matrix that shows the relationship between two classes of objects
incidence matrix that corresponds to a loop is all zero, unless the graph is signed and the loop is negative; then the column is all zero except for
Incidence_matrix
Infinite matrices with Pascal's triangle as elements
In matrix theory and combinatorics, a Pascal matrix is a matrix (possibly infinite) containing the binomial coefficients as its elements. It is thus an
Pascal_matrix
Idempotent linear transformation from a vector space to itself
{\displaystyle I_{r}} is the identity matrix of size r {\displaystyle r} , 0 d − r {\displaystyle 0_{d-r}} is the zero matrix of size d − r {\displaystyle d-r}
Projection_(linear_algebra)
Matrices similar to diagonal matrices
linear algebra, a square matrix A {\displaystyle A} is called diagonalizable or non-defective if it is similar to a diagonal matrix. That is, if there exists
Diagonalizable_matrix
Square matrix whose off-diagonal entries are nonnegative
mathematics, a Metzler matrix is a matrix in which all the off-diagonal components are nonnegative (equal to or greater than zero): ∀ i ≠ j x i j ≥ 0. {\displaystyle
Metzler_matrix
Binary operation, takes two matrices and returns a scalar
_{\mathrm {F} }=\|\mathbf {A} \|_{\mathrm {F} }^{2}\geq 0} , and is zero for a zero matrix, ⟨ A , A ⟩ F = 0 ⟺ A = 0 {\displaystyle \langle \mathbf {A} ,\mathbf
Frobenius_inner_product
Square matrix whose off-diagonal entries are nonpositive
entries are greater than zero. M-matrices have several equivalent definitions, one of which is as follows: a Z-matrix is an M-matrix if it is nonsingular
Z-matrix_(mathematics)
Family of linear error-correcting codes
length 2r − 1. The parity-check matrix of a Hamming code is constructed by listing all columns of length r that are non-zero, which means that the dual code
Hamming_code
In mathematics, a totally positive matrix is a square matrix in which all the minors are positive: that is, the determinant of every square submatrix
Totally_positive_matrix
ZERO MATRIX
ZERO MATRIX
Male
Croatian
, a stone.
Boy/Male
Arabic
Empty.
Boy/Male
Biblical
Root, that straitens or binds, that keeps tight.
Male
Finnish
Finnish form of German Erich, EERO means "ever-ruler."Â
Girl/Female
Assamese, Indian
Rounded
Male
Finnish
Short form of Finnish Antero, TERO means "man; warrior."
Girl/Female
African, Australian, French, Greek, Hebrew, Kurdish, Swahili
Seed
Male
Spanish
Spanish name derived from Latin juniperus, JUNÃPERO means "juniper tree."
Boy/Male
American, Australian, German, Jamaican, Latin
Strong; Vigorous; Powerful; Wise Warrior
Male
Italian
 Short form of Italian Raniero, NERO means "wise warrior." Compare with another form of Nero.
Biblical
root; that straightens or binds; that keeps tight
Female
Greek
(ἩÏá½¼) Greek name derived form the word hÄ“rÅs, HERO means "hero." In mythology, this is the name of the lover of Leandros (Latin Leander).
Boy/Male
Arabic, Australian, German, Greek, Kurdish
Empty; Void
Boy/Male
Australian, French, German, Greek, Italian, Portuguese
Rock; Stone
Male
African
builder; or fierce.
Girl/Female
Latin Greek Shakespearean
Daughter of Priam.
Boy/Male
Greek
Rock.
Boy/Male
African, Finnish, German
The Lord is Exalted
Girl/Female
Latin
Mother of Asopus.
Biblical
crack; leak; distillation; balm
ZERO MATRIX
ZERO MATRIX
Boy/Male
Aramaic
Ploughman.
Girl/Female
Muslim
Boy/Male
Afghan, African, Indian, Sanskrit
He Fights for What is his; Of Noble Birth
Male
Italian
Italian form of Latin Hugo, UGO means "heart," "mind," or "spirit."
Female
Scottish
Scottish Gaelic form of French Jeanette, SÃŒNEAG means "God is gracious."Â
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Oriya, Telugu
Advise; King
Boy/Male
Bengali, Hindu, Indian
Formless; Nirakar
Boy/Male
Shakespearean
King Henry V' Officer in the King's army.
Girl/Female
Teutonic
Armored battle maiden.
Girl/Female
Indian, Kannada
Made of Oak
ZERO MATRIX
ZERO MATRIX
ZERO MATRIX
ZERO MATRIX
ZERO MATRIX
v. t.
To render worthy; to exalt into a hero.
n.
A man of distinguished valor or enterprise in danger, or fortitude in suffering; a prominent or central personage in any remarkable action or event; hence, a great or illustrious person.
superl.
Able; strong; valiant; redoubtable; as, a doughty hero.
n.
The point from which the graduation of a scale, as of a thermometer, commences.
pl.
of Zero
n.
Fig.: The lowest point; the point of exhaustion; as, his patience had nearly reached zero.
pl.
of Hero
n.
The character or personality of a hero.
n.
That which has no value; a cipher; zero.
n.
The common cero; also, the spotted cero. See Cero.
n.
The art of calculating by nine figures and zero.
pl.
of Zero
n.
An illustrious man, supposed to be exalted, after death, to a place among the gods; a demigod, as Hercules.
n.
A cipher; nothing; naught.
n.
A large and valuable fish of the Mackerel family, of the genus Scomberomorus. Two species are found in the West Indies and less commonly on the Atlantic coast of the United States, -- the common cero (Scomberomorus caballa), called also kingfish, and spotted, or king, cero (S. regalis).
n.
A cipher; zero.
n.
A Roman emperor notorius for debauchery and barbarous cruelty; hence, any profligate and cruel ruler or merciless tyrant.
a.
Resembling Achilles, the hero of the Iliad; invincible.
n.
The principal personage in a poem, story, and the like, or the person who has the principal share in the transactions related; as Achilles in the Iliad, Ulysses in the Odyssey, and Aeneas in the Aeneid.