Student[LinearAlgebra][BilinearForm] - compute the general bilinear form of two Vectors relative to a Matrix
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Calling Sequence
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BilinearForm(U, V, A, options)
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Parameters
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U, V
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-
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Vectors
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A
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(optional) Matrix; defines the bilinear form
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options
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-
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(optional) parameters; for a complete list, see LinearAlgebra[BilinearForm]
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Description
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Orientation of U
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Orientation of V
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Result
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column
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column
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row
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column
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row
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row
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column
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row
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Note: The orientation of V solely determines whether the Matrix A is transposed.
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If A is omitted, then it defaults to the identity Matrix, and the bilinear form is the dot product.
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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.
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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.
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Examples
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