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

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MathWorks Support Team 2009-6-27

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采纳的回答： MathWorks Support Team

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?

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Answer 1

MathWorks Support Team 2019-3-1

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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.