PseudoInverse Matrix VI

The m-by-n matrix A⁺ is called the pseudoinverse of matrix A if A⁺ satisfies the following four Moore-Penrose conditions:

• A A⁺ A = A.
• A⁺ A A⁺ = A⁺.
• A A⁺ is a symmetric matrix.
• A⁺ A is a symmetric matrix.

The VI computes PseudoInverse Matrix A⁺ using the SVD algorithm. For example, assume the singular value decomposition of A equals USV*. Then A⁺ = VS⁺U*. You can calculate the pseudoinverse matrix of a diagonal matrix S by taking the reciprocal of each element on the diagonal. When the elements are smaller than the tolerance, this VI sets the reciprocals to zero.

The pseudoinverse provides a least-squares solution to a system of linear equations. For example, for a linear system Ax = b, the following equation is the least-squares solution: x = A⁺b.

Examples

Refer to the following example files included with LabVIEW.

• labview\examples\Mathematics\Linear Algebra\Linear Algebra Calculator.vi