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Exercise 3.C.3

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Proof. Use the same notation from 3.22. Extend $T v_{1}, \dots, T v_{n}$ to a basis $T v_{1}, \dots, T v_{n}, w_{1}, \dots, w_{k}$ of $W$ . It is easy to see now that the matrix of $T$ with respect to this basis and the basis $v_{1}, \dots, v_{n}, u_{1}, \dots, u_{m}$ of $V$ satisfies the desired property. □

celiopassos

2017-10-06 00:00

Exercise 3.C.3

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