GINV Function

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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

$Y= {X \beta} +{\epsilon}$

can be performed by using

   b=ginv(x)*y;

as the estimate of ${\beta}$ . This solution has minimum b'b among all solutions minimizing ${\epsilon}^'{\epsilon}$ ,where ${\epsilon} = Y - {Xb}$ .

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.

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