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Let A be an n n symmetric matrix. The optimization problem to maximize x T A x subject to x = 1 has a solution
Let A be an n n symmetric matrix. The optimization problem to maximize xTAx subject to x=1 has a solution v1 . v1 is an eigenvector of A.
Then consider the optimization problem:
maximize xTAx subject to x=1 and <x,v1>=0. This problem has a solution v2 .
a) Show that v2 is an eigenvector of A that is orthogonal to v1.
b) Consider the optimization problem: maximize xTAx subject to x=1 and <x,v1>=0 and <x,v2>=0 . This problem has a solution v3.
Show that v3 is an eigenvector of A that is orthogonal to v1 and v2 .
Thank you!
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