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Instant-use add-on functions for the Wolfram Language
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Determine whether a set of vectors is linearly independent
ResourceFunction["LinearlyIndependent"][{vect1,vect2,…}] returns the conditions under which the given vectors are mutually linearly independent. |
Test some two-dimensional vectors for linear independence:
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Test some three-dimensional vectors for linear independence:
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This set of vectors is linearly dependent:
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Confirm that the third vector can be written as a linear combination of the first two:
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LinearlyIndependent works with any number of vectors of any dimension:
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For vectors with symbolic parameters, LinearlyIndependent may return a ConditionalExpression:
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A True/False result may be obtained by giving values to the parameters:
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LinearlyIndependent accepts vectors with complex components:
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A set of vectors is linearly independent if and only if the rank of the row matrix composed of the vectors equals the length of the vectors:
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A set of vectors is linearly independent if and only if the rank of the row matrix composed of the vectors has a zero-dimensional null space:
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Or, alternatively:
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A set of vectors is linearly independent if and only if the rank of the row matrix composed of the vectors has a nonzero determinant:
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A set of vectors is linearly independent if and only if its row-reduced form has a no zeros along its diagonal:
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The zero vector is linearly dependent on every other vector:
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LinearlyIndependent will not evaluate if the vectors do not all have the same length:
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