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Symbolic singular value decomposition.
sigma = svd(A) sigma = svd(vpa(A)) [U,S,V] = svd(A) [U,S,V] = svd(vpa(A))
sigma = svd(A) is a symbolic vector containing the singular values of a symbolic matrix A.
sigma = svd(vpa(A)) computes 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 whose columns are the singular vectors and a diagonal matrix S containing the singular values. Together, they satisfy A = U*S*V'.
Symbolic singular vectors are not available.
The statements
digits(3) A = sym(magic(4)); svd(A) svd(vpa(A)) [U,S,V] = svd(A)return
[ 0] [ 34] [ 2*5^(1/2)] [ 8*5^(1/2)] [ .311e-6*i] [ 4.47] [ 17.9] [ 34.1] U = [ -.500, .671, .500, -.224] [ -.500, -.224, -.500, -.671] [ -.500, .224, -.500, .671] [ -.500, -.671, .500, .224] S = [ 34.0, 0, 0, 0] [ 0, 17.9, 0, 0] [ 0, 0, 4.47, 0] [ 0, 0, 0, .835e-15] V = [ -.500, .500, .671, -.224] [ -.500, -.500, -.224, -.671] [ -.500, -.500, .224, .671] [ -.500, .500, -.671, .224]
digits, eig, vpa