5.27 Use the facts that for any symmetric matrix A, we have min(A) = inf|x|=1(x Ax/x...

5.27 Use the facts that for any symmetric matrix A, we have λmin(A) =

inf|x|=1(x



Ax/x



x) and λmax(A) = sup|x|=1(x



Ax/x



x) to prove the following string of inequalities. For any symmetric matrices A, B, we have

λmin(A) + λmin(B)

≤ λmin(A + B)

≤ λmin(A) + λmax(B)

≤ λmax(A + B)

≤ λmax(A) + λmax(B).