svd - Compute singular value decomposition of symbolic matrix
Syntax
sigma = svd(A)
sigma = svd(vpa(A))
[U, S, V] = svd(A)
[U, S,
V] = svd(vpa(A))
Description
sigma = svd(A) returns a symbolic vector
containing the singular values of a symbolic matrix A.
With symbolic inputs, svd does not accept complex
values as inputs.
sigma = svd(vpa(A)) returns a vector with
the numeric singular values using variable precision arithmetic.
[U, S, V] = svd(A) and [U, S,
V] = svd(vpa(A)) return numeric unitary matrices U and V with
the columns containing the singular vectors and a diagonal matrix S containing
the singular values. The matrices satisfy A = U*S*V'.
The svd command does not compute symbolic singular
vectors. With multiple outputs, svd does not accept
complex values as inputs.
Examples
Compute the symbolic and numeric singular values and the numeric
singular vectors of the following magic square:
digits(5)
A = sym(magic(4));
svd(A)
svd(vpa(A))
[U, S, V] = svd(A)
The results are:
ans =
0
2*5^(1/2)
8*5^(1/2)
34
ans =
34.0
17.889
4.4721
2.8024*10^(-7)
U =
[ 0.5, 0.67082, 0.5, 0.22361]
[ 0.5, -0.22361, -0.5, 0.67082]
[ 0.5, 0.22361, -0.5, -0.67082]
[ 0.5, -0.67082, 0.5, -0.22361]
S =
[ 34.0, 0, 0, 0]
[ 0, 17.889, 0, 0]
[ 0, 0, 4.4721, 0]
[ 0, 0, 0, 0]
V =
[ 0.5, 0.5, 0.67082, 0.22361]
[ 0.5, -0.5, -0.22361, 0.67082]
[ 0.5, -0.5, 0.22361, -0.67082]
[ 0.5, 0.5, -0.67082, -0.22361]See Also
digits | eig | inv | vpa
 | subs (sym) | | sym |  |
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