Recent content by hayu601

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

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?

Is it true if I state: σmax(A-B) <= σmax(A) - σmin(B) ? I verify numerically that it is correct but how to prove it?

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

It means that every bi element B is not linear combination of vectors in D

Suppose B = {b1,...,bn} and C={c1,...,cn} both are basis set for space V. D = {d1,...,dn} is basis for space T. If B and D is linearly independent, is C and D always independent too? How can we prove (disprove) it?