Using noncommutative Gröbner bases in solving partially prescribed matrix inverse completion problems (Q5955656)

The author investigates the use of noncommutative Gröbner bases in solving partially prescribed matrix inverse completion problems. The author describes a general method by which all block matrix completion problems may be analyzed if sufficient computational power is available. The method is demonstrated with an analysis of all \(3\times 3\) block matrix inverse completion problems with 11 blocks known and 7 unknown. The solutions to all such problems are of a relatively simple form.NEWLINENEWLINENEWLINEA more detailed analysis of a particular problem from the 31824 \(3\times 3\) block matrix completion problems with 11 blocks known and 7 unknown is also performed. A solution to this problem is presented.