compute the general bilinear form of two Vectors relative to a Matrix
BilinearForm(U, V, A, options)
(optional) Matrix; defines the bilinear form
(optional) parameters; for a complete list, see LinearAlgebra[BilinearForm]
The BilinearForm(U, V, A) command computes the product U'⁢.A.V', where U' is either U or its transpose, U%T, and V' is either V or its transpose, V%T, according to the following rules:
Orientation of U
Orientation of V
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.
U ≔ 4|3|2
U ≔ 432
V ≔ 1,2,3,4
V ≔ 1234
A ≔ 1,5,w|2,6,x|3,7,y|4,8,z
A ≔ 12345678wxyz
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