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Analytic function of a matrix
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, every <a href="/facts/Analytic_function/JhL3z8FP">analytic function</a> can be used for defining a matrix function that maps <a href="/facts/Square_matrices/5TP9mNNn">square matrices</a> with complex entries to square matrices of the same size. </p><p>This is used for defining the <a href="/facts/Exponential_of_a_matrix/WID5cG2g">exponential of a matrix</a>, which is involved in the <a href="/facts/Closed-form_expression/y0xCXlSk">closed-form</a> solution of systems of <a href="/facts/Linear_differential_equation/nLEbIIVf">linear differential equations</a>. </p>