Finds the inverse or pseudo-inverse of a matrix

dst = cv.invert(src)
[dst,d] = cv.invert(...)
[...] = cv.invert(..., 'OptionName',optionValue, ...)

Input

• src input floating-point M x N matrix.

Output

• dst output matrix of N x M size and the same type as src.
• d Output value depending on the method. See below.

Options

• Method Inversion method, default 'LU'. One of the following:
  • LU Gaussian elimination with the optimal pivot element chosen.
  • SVD Singular value decomposition (SVD) method. The matrix can be singular.
  • Cholesky Cholesky decomposion. The matrix must be symmetrical and positively defined.

The function cv.invert inverts the matrix src and stores the result in dst. When the matrix src is singular or non-square, the function computes the pseudo-inverse matrix (the dst matrix) so that norm(src*dst - I) is minimal, where I is an identity matrix.

In case of the 'LU' method, the function returns non-zero value if the inverse has been successfully calculated and 0 if src is singular.

In case of the 'SVD' method, the function returns the inverse condition number of src (the ratio of the smallest singular value to the largest singular value) and 0 if src is singular. The SVD method calculates a pseudo-inverse matrix if src is singular.

Similarly to 'LU', the method 'Cholesky' works only with non-singular square matrices that should also be symmetrical and positively defined. In this case, the function stores the inverted matrix in dst and returns non-zero. Otherwise, it returns 0.