The BilinearForm(U, V, A) command computes the product , where  is either U or its transpose, , and  is either V or its transpose, , according to the following rules:

Note: The orientation of V solely determines whether the Matrix A is transposed.

If the conjugate option is specified, or globally set through the SetDefault command, the rules are slightly different.  See LinearAlgebra[BilinearForm] for details.

If A is omitted, then it defaults to the identity Matrix, and the bilinear form is the dot product.

The dimensions of U, V, and A must be such that the product can be formed.  In particular, if A is not included in the calling sequence for bilinear form, U and V must have the same dimension.

By default in the Student[LinearAlgebra] package, complex conjugates are not used when forming dot products, including when computing bilinear forms.  This behavior can be modified with the SetDefault command.