orthogonal transformation of matrix


by vabamyyr
Tags: matrix, orthogonal, transformation
vabamyyr
vabamyyr is offline
#1
Apr6-06, 04:34 PM
P: 66
I have a question on matrix norms and orthogonal transformations. The 2-norm in invariant under orthogonal transformation, for if Q^T*Q=I. But i have trouble showing that for orthogonal Q and Q^H with appropriate dimensions

|| Q^H*A*Q ||2 =|| A ||2
Phys.Org News Partner Science news on Phys.org
NASA's space station Robonaut finally getting legs
Free the seed: OSSI nurtures growing plants without patent barriers
Going nuts? Turkey looks to pistachios to heat new eco-city
doodle
doodle is offline
#2
May23-06, 07:49 AM
P: 161
The 2-norm of A returns the square-root of the maximum absolute eigenvalues of A^HA. So check, does (Q^HA*Q)^HQ^HA*Q preserve the absolute eigenvalues of A^HA?


Register to reply

Related Discussions
orthogonal transformation Calculus & Beyond Homework 2
Orthogonal Matrix Calculus & Beyond Homework 3
orthogonal transformation Calculus & Beyond Homework 2
Is an orthogonal transformation a tensor? Differential Geometry 0