Matrix Inequality: Is BTB <= B1TB1?

[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?

 

[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?