منابع مشابه
Differentiability of Functions of MatricesMatrix Functions DIFFERENTIABILITY OF FUNCTIONS OF MATRICES
A. Let f be a function on the set of diagonal n × n matrices, and let˜f be the unique extension of f to the set of symmetric n × n matrices invariant with respect to conjugation by orthogonal matrices. We show that˜f has the same regularity properties as f.
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lim h→0 f(z + h)− f(z) h if this limit exists. If the derivative of f exists at z, we denote its value by f ′(z), and we say f isholomorphic at z. If f is holomorphic at every point of an open set U we say that f is holomorphic on U . This definition naturally leads to several basic remarks. First, the definition formally looks identical to the limit definition of a derivative of a function of ...
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ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 1961
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm-8-1-81-82