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Matrix representation of a bilinear form

As usual, it is useful to think about how a bilinear form looks like in terms of vectors and matrices.

Unlike a linear form, which was a vector, because it has two inputs, the bilinear form is represented by a matrix

M

which encodes the value for each possible pair of basis vectors.

In terms of that matrix, the form

B (x, y)

is then given by:

B (x, y) = x^{T} M y

Table of contents 223 1
- Effect of a change of basis on the matrix of a bilinear form ( $B_{2} = C^{T} B C$ ) Matrix representation of a bilinear form 157

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