Question: Show that the function defined in the previous example is bilinear. There is an intimate relationship between bilinear functionals and matrices, paralleling the relationship between

Show that the function defined in the previous example is bilinear. There is an intimate relationship between bilinear functionals and matrices, paralleling the relationship between linear functions and matrices (theorem 3.1). The previous example shows that every matrix defines a bilinear functional. Conversely, every bilinear functional on finite dimensional spaces can be represented by a matrix.

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