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svd


Singular Value Decomposition.


Syntax


s = svd(M)
[U, S, V] = svd(M)
[U, S, V] = svd(M, 0)
[U, S, V] = svd(M, 'econ')

Input argument


M

a numeric value: matrix (double or single)

Output argument


s

real vector (singular values) by descending order.

U

left singular values.

S

real diagonal matrix (singular values)

V

right singular values.

Description


[U, S, V] = svd(M) produces a diagonal matrix S of the same dimension as M and with nonnegative diagonal elements in decreasing order, and unitary matrices U and V so that X = U*S*V'.

[U, S, V] = svd(M, 0) produces the 'economy size' decomposition. If M is m-by-n with m > n then only the first n columns of U are computed and S is n-by-n.

[U, S, V] = svd(M,0) produces a different economy-size decomposition of m-by-n matrix M. If m > n then svd(M, 0) is equivalent to svd(M,'econ'). If m <= n then svd(M, 0) is equivalent to svd(M).

Example


X = eye(3, 3);
s = svd(X)
[U, S, V] = svd(X)

See also


eig.

History


Version Description
1.0.0 initial version

Author


Allan CORNET

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