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→Diagonalizable matrices: D was non-italic, but it should have been Tags: Mobile edit Mobile app edit Android app edit |
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where <math>\lambda_\pm</math> are the eigenvalues of its characteristic equation, {{math|1={{!}}''A'' − ''λI''{{!}} = 0}}, and are given by
<math display="block">\lambda_\pm = \frac{tr(A)}{2} \pm \sqrt{\left (\frac{tr(A)}{2}\right )^2 - |A|} .</math>
However, if there is degeneracy, the following formula is used, where f' is the derivative of f.
<math display="block">f(A) = f \left( \frac{tr(A)}{2} \right) I + \mathrm{adj} \left( \frac{tr(A)}{2}I - A \right ) f' \left( \frac{tr(A)}{2} \right) .</math>
=== Examples ===
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==References==
* {{cite book|last1=Higham|first1=Nicholas J.|title=Functions of matrices theory and computation|date=2008|publisher=Society for Industrial and Applied Mathematics|___location=Philadelphia|author-link=
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