# Matrix inequality

1. Jan 20, 2012

### hayu601

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

Can we say something about the relation between BTB and B1TB1?

For example, is it correct if I say BTB <= B1TB1?

2. Jan 20, 2012

### marcusl

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?