Analytic function of a matrix: Difference between revisions

Revision as of 10:49, 29 May 2020

Revision as of 14:35, 29 May 2020

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If the matrix {{mvar|A}} is [[diagonalizable matrix|diagonalizable]], the problem may be reduced to an array of the function on each eigenvalue.

This is to say we can find a matrix {{mvar|P}} and a [[diagonal matrix]] {{mvar|D}}

such that <math>A = P\cdot~ D\cdot~ P^{-1}</math>.

Applying the power series definition to this decomposition, we find that {{math|''f''(''A'')}} is defined by

:<math>f(A) = P \begin{bmatrix}