The powers A k approach zero if all
Chapter 5, Problem 5.3.29(choose chapter or problem)
The powers A k approach zero if all |i | < 1, and they blow up if any |i | > 1. Peter Lax gives four striking examples in his book Linear Algebra. A = " 3 2 1 4# B = " 3 2 5 3 # C = " 5 7 3 4 # D = " 5 6.9 3 4 # kA 1024k > 10700 B 1024 = I C1024 = C kD 1024k < 1078 Find the eigenvalues = e i of B and C to show that B 4 = I and C 3 =
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