Matrix Inequality: Is BTB <= B1TB1?

Thread starter hayu601
Start date Jan 20, 2012
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Inequality Matrix

Jan 20, 2012

hayu601

I am puzzled about this simple case,

Suppose we have (A+B)^T(A+B) <= (A+B1)^T(A+B1),

Can we say something about the relation between B^TB and B1^TB1?

For example, is it correct if I say B^TB <= B1^TB1?

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Jan 20, 2012

marcusl

Science Advisor

Expand all the terms on each side. You'll see that
A^T A
cancels, leaving three additional terms on each side. Does your hypothesis follow?

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