SVD Decomposition VI
- Updated2025-07-30
- 2 minute(s) read
Computes the singular value decomposition (SVD) of the m × n matrix A. Wire data to the A input to determine the polymorphic instance to use or manually select the instance.
The following equation defines the singular value decomposition of matrix A for real cases:
A = USVTThe following equation defines the singular value decomposition of matrix A for complex cases:
A = USVHIn the previous two equations, the columns in U and V are orthogonal, and S is a diagonal matrix whose diagonal elements are the singular values of A in descending order.
Because the singular values of matrix A are the nonnegative square roots of the eigenvalues of AHA, they all are nonnegative. The diagonal matrix S is unique for a given matrix.
If r represents the rank of A, the number of nonzero singular values of A is r, the first r columns in U are the normal orthogonal bases of the column space of A, and the first r columns in V are the normal orthogonal bases of the row space of A.
You can use SVD decomposition to solve linear algebra problems, such as the pseudoinverse of a matrix, total least-squares minimization, and matrix approximation. SVD factorization also is useful in image processing applications, such as image compression.