On differentiability of the matrix trace operator and its applications (Q2704395)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On differentiability of the matrix trace operator and its applications |
scientific article |
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2 July 2001
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differentiability
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matrix trace operator
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trace derivatives
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On differentiability of the matrix trace operator and its applications (English)
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The authors study the trace derivatives of matrices, \(\partial \text{ tr}\{f(X)\}/\partial X\), obtaining that \(\partial \text{ tr}\{f(X)\}\) \(/\partial X=[M_2(X)M_1(X)]^T\) as \(f(X+ \varepsilon \Delta X)-f(X)= \varepsilon M_1(X)\Delta X M_2(X)\), \( \varepsilon\to 0\). The list of the most common derivatives is given.
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