Syntax
where I1 and I2 are valid belief store numbers and B1 and B2 are
the names of bases or elements.
The INVERT: command is used to calculate the Moore-Penrose
generalised inverse of a real symmetric matrix. For nonsingular
matrices, this yields the usual matrix inverse. (For nonsingular
matrices, the algorithm employed may be somewhat inefficient.)
In the first form of the syntax, the variance matrix specified over B1
in belief store I1 is taken; its generalised inverse calculated; and
then this generalised inverse overwrites the original. In the second
form of the syntax, the calculated generalised inverse is stored instead
as though it were a variance matrix specified over the collection B2. In this
case the two collections B1 and B2 need not be disjoint, but they do
need to be of the same dimension.
The third and fourth forms of the syntax repeat the first and second
respectively, except that the original matrix is transformed into
correlation form before the generalised inverse is calculated. The
generalised inverse is then stored as required.
The INVERT: command is unaffected by the LOCK: command.
Supposing that the matrix to be inverted is V of dimension
n, the pseudo-inverse obtained is
, where
is the diagonal matrix of ordered eigenvalues of V,
and
has the non-zero diagonal elements inverted; and where R
is the matrix of corresponding orthonormal eigenvectors. The generalised
inverse of the null matrix we take to be the null matrix.
