Wolfram Function Repository
Instant-use add-on functions for the Wolfram Language
Function Repository Resource:
Decompose a vector into a linear combination of a set of vectors
ResourceFunction["LinearCombination"][{u},{vi}] returns a list of coefficients that express u as a linear combination of the basis vectors vi. | |
ResourceFunction["LinearCombination"][{u}, {vi}, type] returns the given representation type that express u as a linear combination of the vi. |
Express a vector as a combination of two vectors:
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Express the output as an Association:
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Display the linear combination as an Inactive expression:
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Verify the decomposition is correct:
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Express a matrix in terms of a set of matrices:
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Verify the decomposition is correct:
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If no linear combination is found, LinearCombination returns unevaluated:
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If the basis set is not linearly independent, LinearCombination will return one combination from the infinite set of possibilities:
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