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MAT #MAXDET(C,dim,S)
finds the principal dim*dim submatrix with the maximal
determinant from a symmetric matrix C.
Indices of rows (and columns) belonging to that
submatrix are saved as a column vector S.

The algorithms for this task are explained in
S. Mustonen: Matrix computations in Survo
(www.helsinki.fi/survo/matrix99.html).
The extended forms of MAT #MAXDET are
MAT #MAXDET(C,dim,S,0) / Exhaustive search
MAT #MAXDET(C,dim,S,1) / Stepwise procedure (default)
MAT #MAXDET(C,dim,S,2) / Improved stepwise procedure
MAT #MAXDET(C,dim,S,3) / N=#_of_replicates, Random search
MAT #MAXDET(C,dim,S,4) / N=# Improved random search

Applications: See also www.helsinki.fi/survo/matrix99.html 
MAT #MAXDET can be applied to determination of a basis of
the column space of a m*n matrix A as follows.
If the rank of A (determined by the SVD of A) is r,
the most orthogonal subset of columns of A as an m*r matrix B
is found by the commands
MAT C=MTM(NRM(A))
MAT #MAXDET(C,r,S)  / or MAT #MAXDET(C,r,S,2), for example
MAT B=SUB(A,*,S)

If A is a factor matrix, the commands
MAT C=MTM(NRM(A'))
MAT #MAXDET(C,n,S) / Find row space of A
MAT B=SUB(A,S,*)
correspond to the cosine rotation of factor analysis
usually performed by
ROTATE A,n / METHOD=COS,0

A = More about additional MAT #operations 
M = More about MAT operations