Svd of inverse matrix

1. How do you find the inverse of a matrix using SVD?
2. What are the singular values of a inverse?
3. Does SVD work for any matrix?
4. How do you find pseudo inverse using SVD?

How do you find the inverse of a matrix using SVD?

There (and subsequently on other places), I've learned that if a SVD is applied to a square matrix M, M=USVT, then the inverse of M is relatively easy to calculate as M−1=VS−1UT.

What are the singular values of a inverse?

The columns of U and V are called the left singular vectors and right singular vectors, respectively. The diagonal entires si are called singular values. The singular values are always ≥ 0.

Does SVD work for any matrix?

Also, singular value decomposition is defined for all matrices (rectangular or square) unlike the more commonly used spectral decomposition in Linear Algebra.

How do you find pseudo inverse using SVD?

We can obtain the pseudoinverse from the SVD by inverting all singular values that are non-zero, and leaving all zero singular values at zero.