Let A be an n n matrix and let be an eigenvalue of A whose eigenspace has dimension k
Chapter 6, Problem 16(choose chapter or problem)
Let A be an n n matrix and let be an eigenvalue of A whose eigenspace has dimension k, where 1 < k < n. Any basis {x1, . . . , xk } for the eigenspace can be extended to a basis {x1, . . . , xn} for Rn. Let X = (x1, . . . , xn) and B = X1AX. (a) Show that B is of the form I B12 O B22 where I is the k k identity matrix. (b) Use Theorem 6.1.1 to show that is an eigenvalue of A with multiplicity at least k. 1
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