GINV Function
computes the generalized inverse
- GINV( matrix)
where matrix is a numeric matrix or literal.
The GINV function creates the Moore-Penrose
generalized inverse of matrix.
This inverse, known as the four-condition
inverse, has these properties:
If G = GINV(A) then
-
AGA = A GAG = G (AG)' = AG (GA)' = GA .
The generalized inverse is also known as the
pseudoinverse, usually denoted by A-.
It is computed using the singular value
decomposition (Wilkinson and Reinsch 1971).
Least-squares regression for the model
![Y= {X \beta} +{\epsilon}](images/i17eq89.gif)
can be performed by using
b=ginv(x)*y;
as the estimate of
.
This solution has minimum b'b among all
solutions minimizing
,where
.Projection matrices can be formed by specifying
GINV(X)*X (row space) or
X*GINV(X) (column space).
See Rao and Mitra (1971) for a discussion
of properties of this function.
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.