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MTM[svd] - compute the singular values of a matrix
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Calling Sequence
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S = svd(A)
[U,S,V] = svd(A)
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Parameters
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A
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matrix, vector, array, or scalar
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Description
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The function svd(A) computes the singular values and left and right singular vectors of matrix A.
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When the function is called using the form S = svd(A), the returned value of S is a column vector containing the singular values of A.
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When the function is called using the form U,S,V := svd(A), the returned value of U is a matrix whose columns are the left singular vectors of A. The returned value of S is a column vector containing the singular values of A. The returned value of V is a matrix whose columns are the right singular vectors of A.
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Examples
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![A := Matrix([[1, 2, 1], [2, 4, 2], [2, 8, 1]])](/support/helpjp/helpview.aspx?si=7693/file04882/math88.png)
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![A := Matrix([[1, 2, 1], [2, 4, 2], [2, 8, 1]])](/support/helpjp/helpview.aspx?si=7693/file04882/math91.png)
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*(198+2*8741^(1/2))^(1/2)], [(1/2)*(198-2*8741^(1/2))^(1/2)]])](/support/helpjp/helpview.aspx?si=7693/file04882/math98.png)
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![U, S, V := Matrix([[-.241424496932006, -.376449481711859, -.894427190999916], [-.482848993864012, -.752898963423719, .447213595499958], [-.841766631202282, .539841586573655, -0.315964496254882e-16]]), Matrix([[9.81053809097800, 0, 0], [0, 1.65931985026082, 0], [0, 0, 0.329629655349925e-15]]), Matrix([[-.294648032580691, -.483670604727494, -.824163383692134], [-.932505223882814, .334015093825057, .137360563948689], [-.208845742900333, -.809009680547506, .549442255794756]])](/support/helpjp/helpview.aspx?si=7693/file04882/math105.png)
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