Linear Algebra

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: spans . Thus fi is a basis for , and so = W1 ⊕ · · · ⊕ . 5.4.13 Suppose that W is the T-cyclic subspace of generated by v and that w ∈ . Since W = span({ (v) T 2 (v) }), this means that there exists an integer n and a0 1 ∈ such that w = a0 + n(v) = (a + a + · · · + a Tn)(v). Setting g(t) = a1 (v) + · · · + anT 0 1 n a0 + a1 + · · · + antn, we have that w = g(T)(v). 5.4.17 Let f (t) = ± + cn−1 −1 + c 1 + c0 . By the Cayley-Hamilton Theorem, f ( ) = 0. In other words, n = ±(cn−1 −1 + ·...
View Full Document

This note was uploaded on 04/02/2013 for the course MATH 115A 262398211 taught by Professor Fuckhead during the Spring '10 term at UCLA.

Ask a homework question - tutors are online