Matrix transformation and inequality

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Homework Help Overview

The discussion revolves around the properties of unitary matrices and positive definite matrices, specifically examining the implications of matrix transformations and inequalities.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the meaning of the inequality between matrices and question the definitions involved, particularly what it means for one matrix to be less than another.

Discussion Status

The conversation is ongoing, with participants seeking clarification on the definitions of matrix inequalities and the relationships between the matrices involved. There is an exploration of the implications of the transformations applied to the matrices.

Contextual Notes

Some participants express uncertainty regarding the notation and definitions used in the context of matrix inequalities, indicating a need for further discussion on these foundational concepts.

hayu601
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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?
 
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hayu601 said:

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
 
A < B means that (B-A) > 0 or (B-A) is positive definite
 
Are you referring to A and B as matricies?
 

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