return a basis for a vector space

Student[LinearAlgebra][Basis] - return a basis for a vector space

Student[LinearAlgebra][IntersectionBasis] - return a basis for the intersection of vector space(s)

Student[LinearAlgebra][SumBasis] - return a basis for the direct sum of vector space(s)

	Calling Sequence
	Basis(V, options) IntersectionBasis(VS, options) SumBasis(VS, options)

Parameters

V	-	Vector, list of Vectors, or set of Vectors
VS	-	list whose elements represent vector spaces; each list element is a Vector or a list or set of Vectors whose span represents the vector space
options	-	(optional) parameters; for a complete list, see LinearAlgebra[Basis]

Description

•	The Basis(V) command returns a list or set of Vectors that forms a basis for the vector space spanned by the original Vectors, in terms of the original Vectors. A basis for the 0-dimensional space is an empty list or set.

If V is a list of Vectors, the Basis(V) command returns a list of Vectors. If V is a single Vector or a set of Vectors, a set of Vectors is returned.

•	The IntersectionBasis(VS) command returns a list or set of Vectors that forms a basis for the intersection of the vector spaces defined by the Vector in each list element of VS. IntersectionBasis([]) returns the empty set.

If all the elements of VS are lists of Vectors, the IntersectionBasis(V) command returns a list of Vectors. Otherwise, a set of Vectors is returned.

•	The SumBasis(VS) command returns a list or set of Vectors that forms a basis for the direct sum of the vector spaces defined by the Vector in each list element of VS. SumBasis([]) returns the empty set.

If all the elements of VS are lists of Vectors, the SumBasis(V) command returns a list of Vectors. Otherwise, a set of Vectors is returned.

•	All Vectors given in the V or VS parameters must have the same dimension and orientation.

Examples

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	See Also
	LinearAlgebra[Basis], Student[LinearAlgebra], Student[LinearAlgebra][GramSchmidt], Student[LinearAlgebra][LUDecomposition], Student[LinearAlgebra][NullSpace], Student[LinearAlgebra][RowSpace]