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Linear Algebra

Exercise 2.1.27

Answers

1.: Let ${v_{1}, v_{2}, \dots, v_{k}}$ be a basis for $W$ and we can extend it to a basis $β = {v_{1}, v_{2}, \dots, v_{n}}$ of $V$ . Then we may set $W^{'} =$ span $({v_{k + 1}, v_{k + 2}, \dots, v_{n}})$ . Thus we have $V = W \oplus W^{'}$ and we can define $T$ be the projection on $W$ along $W^{'}$ .
2.: The two projection in Exercise 2.1.24 would be the example.

jephianlin

2011-06-27 00:00

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