Wolfram Function Repository
Instant-use add-on functions for the Wolfram Language
Function Repository Resource:
Find a basis for the subspace spanned by a list of vectors
ResourceFunction["SubspaceBasis"][vecs] returns a basis for the subspace spanned by vecs. | |
ResourceFunction["SubspaceBasis"][polys,x,"Polynomial"] returns a basis for the subspace spanned by a list of polynomials in x. | |
ResourceFunction["SubspaceBasis"][funcs,x] returns a basis for the subspace spanned by a list of functions of x. |
A basis for the subspace spanned by a dependent list of vectors in ℝ4:
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If the vectors in the list are independent, then SubspaceBasis[list] returns a list:
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Test whether a list of vectors is independent (compare with ResourceFunction["LinearlyIndependent"]):
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A basis for the subspace spanned by a dependent list of three 2×2 matrices:
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The 2×2 symmetric matrices together with the 2×2 trace zero matrices do not form an independent list of matrices:
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A basis for the span of this list of matrices:
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A basis for the subspace spanned by a dependent list of polynomials in x:
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A basis for the subspace spanned by a dependent list of trig functions:
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Test that a list of trigonometric polynomials is linearly independent:
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When the input is a set of functions, SubspaceBasis uses a method that may be ill-conditioned:
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Specifying polynomial inputs gives a better result:
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