Science Talk

ga · Guest

Hi,

is there a symbolic form to compute the null space projector without
matrix inversion?

In detail, given a rectangular matrix nxm A it is possible to compute
its null space mxm N with the formula:

N = I - (A^+)A

where I is the mxm Identity matrix and (A^+) is the pseudoinverse of
A, i.e.:

(A^+) = A'inv(A'A)

here A' is the transpose of A.

It would be useful for me to find a formula for N that does not
require matrix inversion, for example using the transpose instead of
the pseudoinverse.

Any comment or suggestion is welcome.

Thanks in advance,
g.