Hi

Let A be an

matrix. An

matrix

is a pseudoinverse of A if there are matrices

such that

Show that

exists and is unique.

Whereas i know pseudo inverse is obtained from singular value decomposition (SVD), as any

matrix can be decomposed as

where

is diagonal matrix and

are orthogonal matrices.

So we can find

this stratifies the first property

.

Where

is matrix of reciprocal of eigenvalues of

.

My Question is how can

1. How can I prove other properties

using this SVD decomposition.

2. Here in the stated problem matrices are not orthogonal, is it OK.

Thanks in advance