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Math · Advanced Math
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B8. Let ARand |I be any subordinate matrix norm.

Recall that A (a) is positive if a 0 for all i and j, which we write as A > 0. For a vector x R, we write20 if 2 0 for al i and 0 if x0 for . We denote by ρ(A)-max(λ| : det(Al-A-0) the spectral radius of A.

(e) Suppose A > 0 with ρ(A)-1 . Show that link→x Ak-G, where G is a rank-one matrix. (You mav assume without proo f that for any square matrix B. link-exBk-0 if ρ(B) < 1)

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