invertibleSubmatrix

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invertibleSubmatrix

$\begin{usage} invertibleSubmatrix(M)(a) \end{usage}$

Signature

invertibleSubmatrix: (M:MatrixCategory %) $\to$ M $\to$ (Boolean, AZ, AZ)

where
AZ == Array MachineInteger

$\begin{params} {\em M} & \htmlref{\texttt{MatrixCategory}}{MatrixCategory} \% & A matrix type\\ {\em a} & M & A matrix\\\end{params}$

$\begin{retval} Returns $(max?, [r_1,\dots,r_r], [c_1,\dots,c_r])$where $r \le \... ...s exactly the rank of $a$\ and the given minor is of maximal size. \end{retval}$

$\begin{remarks} $r$\ can also happen to be the rank of $a$\ when $max?$\ is {\it false}\xspace , but the algorithm was unable to prove it. \end{remarks}$

See Also

maxInvertibleSubmatrix

Manuel Bronstein 2000-12-13