In mathematics, the class of Z-matrices are those matrices whose off-diagonal entries are less than or equal to zero; that is, the matrices of the form:...

In mathematics, a symmetric matrix   M   {\displaystyle \ M\ } with real entries is positive-definite if the real number   x ⊤ M x   {\displaystyle \...

Z-matrix may mean: Z-matrix (chemistry), a table of the locations of atoms comprising a molecule Z-matrix (mathematics), a matrix whose off-diagonal entries...

matrix, K = 1 3 [ Q x x − Q y y − Q z z Q y x + Q x y Q z x + Q x z Q z y − Q y z Q y x + Q x y Q y y − Q x x − Q z z Q z y + Q y z Q x z − Q z x Q z...

In mathematics, the Hessian matrix, Hessian or (less commonly) Hesse matrix is a square matrix of second-order partial derivatives of a scalar-valued...

In mathematics, a unimodular matrix M is a square integer matrix having determinant +1 or −1. Equivalently, it is an integer matrix that is invertible...

In mathematics, the determinant is a scalar-valued function of the entries of a square matrix. The determinant of a matrix A is commonly denoted det(A)...

In mathematics, a Hurwitz matrix, or Routh–Hurwitz matrix, in engineering stability matrix, is a structured real square matrix constructed with coefficients...

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...

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...

In the mathematical discipline of linear algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices...

In mathematics, 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...

In mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function. It is used to solve systems...

In mathematics, especially linear algebra, an M-matrix is a matrix whose off-diagonal entries are less than or equal to zero (i.e., it is a Z-matrix) and...

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

In probability theory and mathematical physics, a random matrix is a matrix-valued random variable—that is, a matrix in which some or all of its entries...

In mathematics, a Q-matrix is a square matrix whose associated linear complementarity problem LCP(M,q) has a solution for every vector q. M is a Q-matrix...

In mathematics, specifically linear algebra, the Woodbury matrix identity – named after Max A. Woodbury – says that the inverse of a rank-k correction...

transformation matrix: S v = [ v x 0 0 0 0 v y 0 0 0 0 v z 0 0 0 0 1 ] . {\displaystyle S_{v}={\begin{bmatrix}v_{x}&0&0&0\\0&v_{y}&0&0\\0&0&v_{z}&0\\0&0&0&1\end{bmatrix}}...

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...

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...

z\\z\end{bmatrix}}} After carrying out the matrix multiplication, the homogeneous component w c {\displaystyle w_{c}} will be equal to the value of z...

In mathematics, an involutory matrix is a square matrix that is its own inverse. That is, multiplication by the matrix A n × n {\displaystyle {\mathbf...

the rings Z / N Z {\displaystyle \mathbb {Z} /N\mathbb {Z} } can be added: ( a + N Z ) + ( b + N Z ) = a + b + N Z {\displaystyle (a+N\mathbb {Z} )+(b+N\mathbb...

In mathematics, the conjugate transpose, also known as the Hermitian transpose, of an m × n {\displaystyle m\times n} complex matrix A {\displaystyle...

In 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 mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation...

In mathematics, every analytic function can be used for defining a matrix function that maps square matrices with complex entries to square matrices of...

In mathematics, rings are algebraic structures that generalize fields: multiplication need not be commutative and multiplicative inverses need not exist...

In 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 ≥...