Ask HN: What if we add first then multiply in matrix multiplication?

Or even replace them with other binary operations?

What if the nature is not multiple=>add as our usually linear algebra, it is actually add=>multiply or subtract=>exponential?

Since subtraction is not commutative, this may explain some non commute behaviour of something.

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Have you tried it? What kind of algebraic structure do you get?

I think end up I will be making a math engine to try every combinations of binary operation in this experiment, if I really want to do this. The more I think, the more this seems doable to me.

The idea is to check if the new operation has nice properties.

For example if we call your new operation x, is it true that

((A x B) x C) = (A x (B) x C)) ???

Almost all useful operations have that property. Check with a few examples of matrices.

Try asking on a stack overflow math forum

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