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Exercise 2.5.14

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Let $V = 𝔽^{n}$ , $W = 𝔽^{m}$ , $T = L_{A}$ , $β$ , and $γ$ be the notation defined in the Hint. Let $β^{'}$ and $γ^{'}$ be the set of column vectors of $Q$ and $P$ respectively. By Exercise 2.5.13 we have that $β^{'}$ and $γ^{'}$ are bases and $Q = {[I]}_{β^{'}}^{β}$ , $P = {[I]}_{γ^{'}}^{γ}$ . Since we have that ${[T]}_{β^{'}}^{γ^{'}} = {[I]}_{γ}^{γ^{'}} {[T]}_{β}^{γ} {[I]}_{β^{'}}^{β}$ , we have that $B = P^{- 1} AQ$ .

jephianlin

2011-06-27 00:00

Exercise 2.5.14

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