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...

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...

maps involving the zero vector space. For example, if A is a 3-by-0 matrix and B is a 0-by-3 matrix, then AB is the 3-by-3 zero matrix corresponding to...

zero matrix of any given size m × n (with entries from a given ring), so when the context is clear, one often refers to the zero matrix. In a matrix ring...

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...

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....

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...

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...

to be positive or zero (that is, nonnegative). Negative-definite and negative semi-definite matrices are defined analogously. A matrix that is not positive...

\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...

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,...

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...

a matrix is the conjugate transpose. The product of a matrix with its adjugate gives a diagonal matrix (entries not on the main diagonal are zero) whose...

algebra, an invertible matrix (non-singular, non-degenerate or regular) is a square matrix that has an inverse. In other words, if a matrix is invertible, it...

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,...

&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 =...

A^{+}} ⁠ of a matrix ⁠ A {\displaystyle A} ⁠, often called the pseudoinverse, is the most widely known generalization of the inverse matrix. It was independently...

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...

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...

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...

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...

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...

theory, the Laplacian matrix, also called the graph Laplacian, admittance matrix, Kirchhoff matrix, or discrete Laplacian, is a matrix representation of a...

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 = [...

such norms are referred to as matrix norms. Matrix norms differ from vector norms in that they must also interact with matrix multiplication. Given a field...

polynomial to zero. In spectral graph theory, the characteristic polynomial of a graph is the characteristic polynomial of its adjacency matrix. In linear...

Ax=0} admits non-zero solutions. These characterizations follow from standard rank-nullity and invertibility theorems: for a square matrix A, d e t ( A )...

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...

triangular matrix with zeros along the main diagonal is nilpotent, with index ≤ n {\displaystyle \leq n} [citation needed]. For example, the matrix B = [ 0...

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"...