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Derivative of matrix square root 
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#1
Dec712, 10:22 PM

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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!



#2
Dec812, 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] 


#3
Dec812, 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)



#4
Dec812, 10:57 AM

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Derivative of matrix square root



#5
Dec912, 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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