In 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...

analysis. Square matrices, matrices with the same number of rows and columns, play a major role in matrix theory. The determinant of a square matrix is a number...

If A is an m × n matrix, then AT is an n × m matrix. In the case of square matrices, AT may also denote the Tth power of the matrix A. For avoiding a...

the square root of a matrix extends the notion of square root from numbers to matrices. A matrix B is said to be a square root of A if the matrix product...

In linear algebra, the trace of a square matrix A, denoted tr(A), is the sum of the elements on its main diagonal, a 11 + a 22 + ⋯ + a n n {\displaystyle...

In mathematics, a triangular matrix is a special kind of square matrix. A square matrix is called lower triangular if all the entries above the main diagonal...

A singular matrix is a square matrix that is not invertible, unlike non-singular matrix which is invertible. Equivalently, an n {\displaystyle n} -by-...

In linear algebra, an orthogonal matrix, or orthonormal matrix, is a real square matrix whose columns and rows are orthonormal vectors. One way to express...

invertible matrix (non-singular, non-degenarate or regular) is a square matrix that has an inverse. In other words, if some other matrix is multiplied...

In linear algebra, an invertible complex square matrix U is unitary if its matrix inverse U−1 equals its conjugate transpose U*, that is, if U ∗ U = U...

In linear algebra, the identity matrix of size n {\displaystyle n} is the n × n {\displaystyle n\times n} square matrix with ones on the main diagonal...

In mathematics, a stochastic matrix is a square matrix used to describe the transitions of a Markov chain. Each of its entries is a nonnegative real number...

probability theory. Bernoulli matrix — a square matrix with entries +1, −1, with equal probability of each. Centering matrix — a matrix which, when multiplied...

In linear algebra, a minor of a matrix A is the determinant of some smaller square matrix generated from A by removing one or more of its rows and columns...

computer science, an adjacency matrix is a square matrix used to represent a finite graph. The elements of the matrix indicate whether pairs of vertices...

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...

In mathematics, an Hadamard matrix, named after the French mathematician Jacques Hadamard, is a square matrix whose entries are either +1 or −1 and whose...

In mathematics, a complex square matrix A is normal if it commutes with its conjugate transpose A*: A  normal ⟺ A ∗ A = A A ∗ . {\displaystyle A{\text{...

In mathematics, a Hermitian matrix (or self-adjoint matrix) is a complex square matrix that is equal to its own conjugate transpose—that is, the element...

is the matrix of all its first-order partial derivatives. If this matrix is square, that is, if the number of variables equals the number of components...

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 = [...

In mathematics, a Hurwitz-stable matrix, or more commonly simply Hurwitz matrix, is a square matrix whose eigenvalues all have strictly negative real part...

covariance matrix (also known as auto-covariance matrix, dispersion matrix, variance matrix, or variance–covariance matrix) is a square matrix giving the...

algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices. There are many different matrix decompositions;...

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...

mathematics, an elementary matrix is a square matrix obtained from the application of a single elementary row operation to the identity matrix. The elementary matrices...

classical adjoint of a square matrix A, adj(A), is the transpose of its cofactor matrix. It is occasionally known as adjunct matrix, or "adjoint", though...

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...

In linear algebra, a symmetric matrix is a square matrix that is equal to its transpose. Formally, A  is symmetric ⟺ A = A T . {\displaystyle A{\text{...

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