Proving σmax(A-B) ≤ σmax(A) - σmin(B)

Thread starter hayu601
Start date May 25, 2012

May 25, 2012

hayu601

Is it true if I state:

σ_max(A-B) <= σ_max(A) - σ_min(B) ?

I verify numerically that it is correct but how to prove it?

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May 25, 2012

HallsofIvy

Science Advisor

Homework Helper

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/

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