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Derivative of matrix square root

by cpp6f
Tags: derivative, matrix, root, square
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cpp6f
#1
Dec7-12, 10:22 PM
P: 4
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
#2
Dec8-12, 06:25 AM
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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]
cpp6f
#3
Dec8-12, 10:13 AM
P: 4
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
#4
Dec8-12, 10:57 AM
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Derivative of matrix square root

Quote Quote by cpp6f View Post
I forgot to mention that A is positive definitive. So the principle square root of A (the square root that is also positive definitive)
See what you can do with the Chain Rule is what you are saying is A(X) is a one parameter family of positive definite square matrices.
bpet
#5
Dec9-12, 09:35 PM
P: 523
To save you a bit of footwork - implicit differentiation on the equation S(x)*S(x)=A(x) shows that S'(x) is the unique solution to a Sylvester equation.


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