# Derivative of matrix square root

## Main Question or Discussion Point

If I have a matrix valued function A(x) of some scalar x, how do I compute the derivative of the square root of A with respect to x? It seems like it should be simple, but I can't find it anywhere on the internet. Thanks!

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tiny-tim
Homework Helper
hi cpp6f!

how would you define the square root of a matrix?

eg the square root of the 2x2 identity matrix could be itself, or [1,0;0,-1]

I forgot to mention that A is positive definitive. So the principle square root of A (the square root that is also positive definitive)

lavinia