About: Analytic function of a matrix

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In 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. This is used for defining the exponential of a matrix, which is involved in the closed-form solution of systems of linear differential equations.

Attributes	Values
rdf:type	Thing
rdfs:label	Maticová funkce (cs) Analytic function of a matrix (en) Funzione di matrice (it) 行列値関数 (ja) Função matricial (pt) Матричная функция (ru) Matrisfunktion (sv) Матрична функція (uk) 矩阵函数 (zh)
rdfs:comment	Maticová funkce je matematické zobrazení, která zobrazuje matice na matice. Některé komplexní funkce , nejčastěji se setkáme s funkcemi je možné rozšířit přirozeným způsobem na maticové funkce. Tento proces se také nazývá funkční kalkulus. Výraz maticová funkce se někdy používá pro libovolné zobrazení z nějaké množiny do množiny matic. (cs) In 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. This is used for defining the exponential of a matrix, which is involved in the closed-form solution of systems of linear differential equations. (en) 行列値関数（ぎょうれつちかんすう、英: matrix-valued functions）とは行列を変数に持つ特殊関数の総称である。 (ja) В математике, матричная функция — это функция, отображающая матрицу в другую матрицу. (ru) Em matemática, uma função matricial é uma função cujo domínio são matrizes. O determinante, o traço e a exponencial matricial são exemplos de funções matriciais cujo domínio são as matrizes quadradas com imagem nos números complexos. O termo também pode ser usado para a generalização de uma função f de escalares, para uma função fM entre matrizes quadradas. Por exemplo, um polinômio p(x) leva naturalmente a uma função p de domínio no conjunto das matrizes quadradas de ordem nxn e contra-domínio no mesmo conjunto. (pt) Inom matematiken är en matrisfunktion en funktion som avbildar en matris på en matris. (sv) Функція матриці — функція, яка відображає одну матрицю у другу матрицю. (uk) 数学上讲，矩阵函数是把矩阵映射到另一个矩阵的函数。 (zh) In algebra lineare si può estendere il concetto di funzione alle matrici quadrate di qualsiasi ordine n attraverso l'associazione di una serie di Maclaurin ad ogni funzione, riducendola a una somma infinita di potenze di matrici: (it)
rdfs:seeAlso	Sylvester's formula
dcterms:subject	Matrix theory Mathematical physics
Wikipage page ID	12691877 (xsd:integer)
Wikipage revision ID	1079410332 (xsd:integer)
Link from a Wikipage to another Wikipage	Scalar multiplication Monotonic function Algebraic Riccati equation Jordan block Complex analysis Analytic function Mathematics Matrix exponential Matrix multiplication Matrix norm Origin (mathematics) Eigenvalue Concave function Convergent series Linear differential equation Closed-form expression Matrix polynomial Matrix sign function Banach space Matrix theory Cauchy's integral formula Trigonometric functions of matrices Loewner order Square matrix Diagonal matrix Jordan normal form Jordan–Chevalley decomposition Radius Hermitian matrix Invertible matrix Mathematical physics Sylvester's formula Holomorphic functional calculus Diagonalizable matrix Divided difference Positive-definite matrix Positive-semidefinite matrix Spectral radius Spectral theorem Square matrices Square root of a matrix Matrix calculus Unitary matrix Trace inequalities Trapezium rule Taylor expansion Matrix logarithm Bounded linear operator Exponential of a matrix Precision (arithmetic)
sameAs	Analytic function of a matrix Analytic function of a matrix Analytic function of a matrix Analytic function of a matrix Analytic function of a matrix Analytic function of a matrix Analytic function of a matrix Analytic function of a matrix Analytic function of a matrix Analytic function of a matrix Analytic function of a matrix Analytic function of a matrix Analytic function of a matrix Analytic function of a matrix
dbp:wikiPageUsesTemplate	dbt:Hair_space dbt:! dbt:Cite_book dbt:Main dbt:Math dbt:Mvar dbt:Reflist dbt:See_also dbt:Short_description dbt:Norm
has abstract	Maticová funkce je matematické zobrazení, která zobrazuje matice na matice. Některé komplexní funkce , nejčastěji se setkáme s funkcemi je možné rozšířit přirozeným způsobem na maticové funkce. Tento proces se také nazývá funkční kalkulus. Výraz maticová funkce se někdy používá pro libovolné zobrazení z nějaké množiny do množiny matic. (cs) In 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. This is used for defining the exponential of a matrix, which is involved in the closed-form solution of systems of linear differential equations. (en)

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