In mathematics, the matrix sign function is a matrix function on square matrices analogous to the complex sign function.[1]
It was introduced by J.D. Roberts in 1971 as a tool for model reduction and for solving Lyapunov and Algebraic Riccati equation in a technical report of Cambridge University, which was later published in a journal in 1980.[2][3]
^Higham, Nicholas J. (2008). Functions of matrices : theory and computation. Society for Industrial and Applied Mathematics. Philadelphia, Pa.: Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104). ISBN 978-0-89871-777-8. OCLC 693957820.
^Roberts, J. D. (October 1980). "Linear model reduction and solution of the algebraic Riccati equation by use of the sign function". International Journal of Control. 32 (4): 677–687. doi:10.1080/00207178008922881. ISSN 0020-7179.
^Denman, Eugene D.; Beavers, Alex N. (1976). "The matrix sign function and computations in systems". Applied Mathematics and Computation. 2 (1): 63–94. doi:10.1016/0096-3003(76)90020-5. ISSN 0096-3003.
and 26 Related for: Matrix sign function information
In mathematics, the matrixsignfunction is a matrixfunction on square matrices analogous to the complex signfunction. It was introduced by J.D. Roberts...
In mathematics, the signfunction or signum function (from signum, Latin for "sign") is a function that returns the sign of a real number. In mathematical...
In mathematics, every analytic function can be used for defining a matrixfunction that maps square matrices with complex entries to square matrices of...
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...
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...
Walsh matrix is a sequency-ordered. Confusingly, different sources refer to either matrix as the Walsh matrix. The Walsh matrix (and Walsh functions) are...
square root of a Markov matrix: eigenvalues and the Taylor series Denman, Eugene D.; Beavers, Alex N. (1976), "The matrixsignfunction and computations in...
optimization, since, given a function of several real variables that is twice differentiable, then if its Hessian matrix (matrix of its second partial derivatives)...
solution of matrix equations. The implementation is based on spectral projection methods, e.g., methods based on the matrixsignfunction and the matrix disk...
covariance matrix (also known as auto-covariance matrix, dispersion matrix, variance matrix, or variance–covariance matrix) is a square matrix giving the...
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 = [...
formula for the Jacobian matrix of the inverse. There are also versions of the inverse function theorem for complex holomorphic functions, for differentiable...
In mathematics, the matrix exponential is a matrixfunction on square matrices analogous to the ordinary exponential function. It is used to solve systems...
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...
best linear approximation to the graph of the original function. The Jacobian matrix is the matrix that represents this linear transformation with respect...
business and project management, a responsibility assignment matrix (RAM), also known as RACI matrix (/ˈreɪsi/) or linear responsibility chart (LRC), is a model...
determinant is a scalar value that is a certain function of the entries of a square matrix. The determinant of a matrix A is commonly denoted det(A), det A, or...
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 mathematics, particularly in matrix theory, a permutation matrix is a square binary matrix that has exactly one entry of 1 in each row and each column...
{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...
In quantum mechanics, a density matrix (or density operator) is a matrix that describes the quantum state of a physical system. It allows for the calculation...
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...
adjugate of a square matrix A is the transpose of its cofactor matrix and is denoted by adj(A). It is also occasionally known as adjunct matrix, or "adjoint"...
product intended for conventional matrix multiplication uses the + and × functions, replacing these with other dyadic functions can result in useful alternative...
{\displaystyle n\times n} matrix, and T {\displaystyle {}^{\mathsf {T}}} denotes matrix transposition. The integral of this Gaussian function over the whole n...
mathematics, a unimodular matrix M is a square integer matrix having determinant +1 or −1. Equivalently, it is an integer matrix that is invertible over...
Global Information