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

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...

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

set of vectors Irregular matrix Matrix calculus – Specialized notation for multivariable calculus Matrix function – Function that maps matrices to matricesPages...

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...

derivative of a scalar function with respect to a matrix, known as the gradient matrix, which collects the derivative with respect to each matrix element in the...

generalization of the scalar logarithm and in some sense an inverse function of the matrix exponential. Not all matrices have a logarithm and those matrices...

In mathematics, the matrix sign function is a matrix function on square matrices analogous to the complex sign function. It was introduced by J.D. Roberts...

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

Matrix mechanics is a formulation of quantum mechanics created by Werner Heisenberg, Max Born, and Pascual Jordan in 1925. It was the first conceptually...

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...

{0} \}.} To state the implicit function theorem, we need the Jacobian matrix of f {\displaystyle f} , which is the matrix of the partial derivatives of...

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

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), det A, or...

optimization, since, given a function of several real variables that is twice differentiable, then if its Hessian matrix (matrix of its second partial derivatives)...

space, the identity function is always continuous. The identity function is idempotent. Identity matrix Inclusion map Indicator function Knapp, Anthony W...

branches of engineering, a transfer function matrix, or just transfer matrix is a generalisation of the transfer functions of single-input single-output (SISO)...

affine map is the composition of two functions: a translation and a linear map. Ordinary vector algebra uses matrix multiplication to represent linear maps...

In linear algebra, the permanent of a square matrix is a function of the matrix similar to the determinant. The permanent, as well as the determinant,...

operator concave functions, and is encountered in operator theory and in matrix theory, and led to the Löwner–Heinz inequality. A function f : I → R {\displaystyle...

business and project management, a responsibility assignment matrix (RAM), also known as RACI matrix (/ˈreɪsi/; responsible, accountable, consulted, and informed)...

In quantum mechanics, a density matrix (or density operator) is a matrix used in calculating the probabilities of the outcomes of measurements performed...

The cross-correlation matrix of two random vectors is a matrix containing as elements the cross-correlations of all pairs of elements of the random vectors...

the mathematical discipline of matrix theory, a Jordan matrix, named after Camille Jordan, is a block diagonal matrix over a ring R (whose identities...

bars (like so:   ‖ A ‖   {\displaystyle \ \|A\|\ } ). Thus, the matrix norm is a function   ‖ ⋅ ‖ : K m × n → R 0 +   {\displaystyle \ \|\cdot \|:K^{m\times...

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

the given matrix—not a variable, unlike λ {\displaystyle \lambda } —so p A ( A ) {\displaystyle p_{A}(A)} is a constant rather than a function.) The Cayley–Hamilton...

algebra, eigendecomposition is the factorization of a matrix into a canonical form, whereby the matrix is represented in terms of its eigenvalues and eigenvectors...

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...

\Theta (u)} are theta functions of modulus k {\displaystyle k} . The associated transfer matrix T {\displaystyle T} thus is a function of u {\displaystyle...