If 1 and 1 are the smallest eigenvalues of A and B, show that the smallest eigenvalue 1
Chapter 6, Problem 6.4.8(choose chapter or problem)
If 1 and 1 are the smallest eigenvalues of A and B, show that the smallest eigenvalue 1 of A+B is at least as large as 1 + 1. (Try the corresponding eigenvector x in the Rayleigh quotients.) Note. 7 and 8 are perhaps the most typical and most important results that come easily from Rayleighs principle, but only with great difficulty from the eigenvalue equations themselves.
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