Non-square Determinant Definition.

May 30, 2022
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I have a definition for non-square determinants. One needs them to compute left or right inverses of non-square matrices.

The definition is as follows: for a row longest matrix do:

1) Develop the determinant as for a square matrix as normal until reaching a sum of 2xp matrices (p > 2).

2) Write each 2xp matrix as a sum of n 2x2 matrices by deleting all combinations of columns such that 2 remains, in each and shifting the remaining columns left and changing the sign of the term to negative if an odd amount of swaps were needed.

3) Compute the sum of 2x2 matrices.

For a column longest matrix:

1) Do as 1) above until reaching a sum of px2 matrices.

2) Do similar to 2) above, only deleting all combinations of rows and shifting the remaining rows to topmost, changing the sign to negative if an odd number of swaps were required.

3) Compute the sum of 2x2 matrices.