derivative of matrix square root


by cpp6f
Tags: derivative, matrix, root, square
cpp6f
cpp6f is offline
#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!
Phys.Org News Partner Science news on Phys.org
SensaBubble: It's a bubble, but not as we know it (w/ video)
The hemihelix: Scientists discover a new shape using rubber bands (w/ video)
Microbes provide insights into evolution of human language
tiny-tim
tiny-tim is offline
#2
Dec8-12, 06:25 AM
Sci Advisor
HW Helper
Thanks
tiny-tim's Avatar
P: 26,167
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
cpp6f is offline
#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
lavinia is offline
#4
Dec8-12, 10:57 AM
Sci Advisor
P: 1,716

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
bpet is offline
#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.


Register to reply

Related Discussions
Find derivative of Square root (x + square root(x + x^(1/2))) Help! Calculus & Beyond Homework 5
Simplifying the Derivative of the Square Root of a Sum Containing a Square Root Precalculus Mathematics Homework 4
Derivative of Square Root Calculus & Beyond Homework 5
derivative of the square root of xy Precalculus Mathematics Homework 2
Derivative of a square root fraction. Calculus 2