svd

svd

In linear algebra, the singular value decomposition (SVD) is a factorization of a real or complex matrix, with many useful applications in signal processing and statistics.

References

• http://en.wikipedia.org/wiki/Singular_value_decomposition

svd(M)

Applications which employ the SVD include computing the pseudoinverse, least squares fitting of data, matrix approximation, and determining the rank, range and null space of a matrix.

Argument M

Matrix

Returns 1. entry

Matrix : The diagonal matrix of singular values (Sigma).

Returns 2. entry

Matrix : The left singular vectors (U).

Returns 3. entry

Matrix : The right singular vectors (V*).

Example

svd([1, 0, 0, 0, 2; 0, 0, 3, 0, 0; 0, 0, 0, 0, 0; 0, 4, 0, 0, 0])

Computes the matrices Sigma (singular values), U (left-singular vectors) and V* (right-singular vectors) of the matrix.

Example

[S, U, V] = svd([1, 0, 0, 0, 2; 0, 0, 3, 0, 0; 0, 0, 0, 0, 0; 0, 4, 0, 0, 0])

Computes the matrices Sigma, U and V* and stores them in the matrices S, U, V.