PseudoInverse Matrix (Not in Base Package)

Finds the PseudoInverse Matrix of a rectangular, real matrix Input Matrix. Details

Input Matrix is a rectangular, real matrix. When A is not a square matrix, or when A is singular, the inverse of A does not exist. You can compute the pseudoinverse of A instead. Using the Inverse Matrix VI to compute is more efficient than using this VI.
tolerance defines a level such that the number of singular values greater than this level is the rank of the Input Matrix. All of the negative tolerance causes an internal tol=max (m,n)||A|| eps to be used, where A represents the Input Matrix, m represents the number of rows in A, n represents the number of columns in A, ||A|| is the 2-norm of A, eps is the smallest, floating point number that can be represented by type double,

eps = 2^(- 52)=2.22e - 16.

The default is –1.

PseudoInverse Matrix is the pseudoinverse matrix of the Input Matrix. If Input Matrix A is square and not singular, then the pseudoinverse is the same as the inverse of a matrix, and the Inverse Matrix VI should be used as a more efficient method of computing the inverse of the Input Matrix. Refer to the Inverse Matrix VI for more information about this VI.
error returns any error or warning condition from the VI.

PseudoInverse Matrix Details

You compute PseudoInverse Matrix by using the SVD algorithm and any singular value less than the tolerance, which are set to zero.

If the m-by-n matrix satisfies the following four Moore-Penrose conditions:

  1. A A = A
  2. A =
  3. A is a symmetric matrix
  4. A is a symmetric matrix

then is called the pseudoinverse of matrix A.