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

engineering. As a differentiable function of a complex variable is equal to the sum function given by its Taylor series (that is, it is analytic), complex analysis...

the matrix valued analogue csgn ⁡ ( A ) {\displaystyle \operatorname {csgn} (A)} . Although the sign function is not analytic, the matrix function is well...

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

such a way that the operations of multiplication and taking the inverse are analytic functions of the matrix entries. Thus SO(n) is for each n a Lie group...

matrix-valued random variables, and can also be extended to more generic cases. The characteristic function always exists when treated as a function of...

convergent on a half-plane, that may give rise to an L-function via analytic continuation. The Riemann zeta function is an example of an L-function, and some...

functional analysis, a linear function is a linear map. In calculus, analytic geometry and related areas, a linear function is a polynomial of degree one or...

sign function or signum function (from signum, Latin for "sign") is a function that has the value −1, +1 or 0 according to whether the sign of a given...

it is a linear function, a polynomial function, a continuous function, a differentiable function, a smooth function, an analytic function, if the multivariate...