(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I am trying to evaluate exp(i*f(A)), where A is a matrix whose eigenvalues are known and real.

2. Relevant equations

You can expand functions of a matrix in a power-series. I think that's the way to get started on this problem. I foresee the exponential of a power-series expansion of f(A) suddenly becoming a product of exponentials of a matrix, which, themselves, are power-series. It sounds ugly, but perhaps some pleasant collapse will happen.

3. The attempt at a solution

Okay, let's try finding power-series expansion of f(A):

[tex]f(A) = \sum\limits_{n = 0}^{n \to \infty } {\frac{{{f^{(n)}}(0)}}{{n!}}{A^n}} = {\rm{oh dear}}...{\rm{unaware of derivatives of f at 0}}{\rm{.}}[/tex]

Hmmm...maybe my idea above is not so great.

I think I am thwarted by the arbitrariness of the function "f(A)". Prior experience suggests arbitrariness is nothing to be afraid of...just an opportunity for higher generality...which is neato.

When you, dear reader, peruse this cry for help, do any suggestions come to your mind for a starting point to evaluating exp(i*f(A))? I just can't seem to bring "A" outside of "f" in order to take advantage of the fact that we know its eigenvalues.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Arbitrary function of a matrix - power-series representation

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