# Homework Help: Singular value

1. May 25, 2012

### hayu601

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?

2. May 25, 2012

### HallsofIvy

If $a\in A$ then $a\le max(A)$
If $b\in B$ then $b\ge min(a)$ so $-b\ge -min(B)$

Adding, $a-b\le max(A)- min(B)$ for all a in A, b in B/