16.-Linear-Algebra-by-Kenneth-Hoffman · Problem 10.2.15

Bilinear Forms

Mathematics — Linear Algebra · dual-basis-inverse-matrix

Problem

Let

V

f

\mathfrak{B}

, and

\mathfrak{B}'

be as in Exercise 13. Suppose

[f]_{\mathfrak{B}} = A

. Show that

\alpha_i' = \sum_j (A^{-1})_{ij} \alpha_j = \sum_j (A^{-1})_{ji} \alpha_j.