Is there a list describing how \ (left division) achieves its result and what matrices it recognizes in MATLAB?

Is there a list describing how \ (left division) achieves its result and what matrices it recognizes in MATLAB?

When using the backslash (\) operator, what classes of square matrices does MATLAB recognize and treat separately?

I know that it determines if the matrix is triangular, but what about diagonal matrices and the identity?

Answer 1

[MathWorks Support Team]

The algorithm for the left-hand division operator is shown at the following:

https://www.mathworks.com/help/releases/R2009a/techdoc/matlab_prog/f0-40063.html

Triangular matrices are recognized and their sets of linear equations are solved by forward or back substitutition. This requires only O(n^2) flops, in contrast to the O(n^3) flops for general matrices.

Diagonal matrices, including the identity, are treated as triangular by the full backslash and as sparse matrices with only 'n' nonzeros by the sparse operations.