Assembly: ImslCS (in ImslCS.dll) Version: 6.5.0.0
Syntax
C# |
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[SerializableAttribute] public class SVD |
Visual Basic (Declaration) |
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<SerializableAttribute> _ Public Class SVD |
Visual C++ |
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[SerializableAttribute] public ref class SVD |
Remarks
SVD is based on the LINPACK routine SSVDC; see Dongarra et al. (1979).
Let n be the number of rows in A and let p be the number of columns in A. For any
n x p matrix A, there exists an n x n orthogonal matrix U and a p x p orthogonal matrix V such that
where , and . The scalars are called the singular values of A. The columns of U are called the left singular vectors of A. The columns of V are called the right singular vectors of A.
The estimated rank of A is the number of that is larger than a tolerance . If is the parameter tol in the program, then
The Moore-Penrose generalized inverse of the matrix is computed by partitioning the matrices U, V and as , and where the "1" matrices are k by k. The Moore-Penrose generalized inverse is .