Matrix transformation and inequality

[hayu601]

Homework Statement

Suppose U and V are unitary matrix, A and B are positive definite,

Does:

UAU^-1 < VBV^-1

implies A < B

and vice versa?

 

[Ray Vickson]

Homework Statement

Suppose U and V are unitary matrix, A and B are positive definite,

Does:

UAU^-1 < VBV^-1

implies A < B

and vice versa?

What do you mean by Y < Z for two matrices Y and Z?

RGV

 

[hayu601]

A < B means that (B-A) > 0 or (B-A) is positive definite

 

[STEMucator]

Are you referring to A and B as matricies?