Let A be an n n matrix such that ||A|| < 1, where the norm is
Question:
(a) Prove that An → O as n → ∞.
(b) Deduce from (a) that I - A is invertible and (I - A)-1 = I + A + A2 + A3 + · · ·
(c) Show that (b) can be used to prove Corollaries 3.35 and 3.36.
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The sum and max norms are operator norms induced from the sum and max norms on R n so they are matri...View the full answer
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