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This is getting close to what I wanted -- thank you. But now you introduce what might be the real heart of it: the definition of matrix multiplication. I know
by shanusmagnus 4y ago
This is getting close to what I wanted -- thank you. But now you introduce what might be the real heart of it: the definition of matrix multiplication. I know the rules of this operation, and how matrix multiplication distinguishes rows and columns, and the geometric interpretation of a vector multiplied by a matrix. But where does that definition come from in the first place?
This might be too ill-posed to answer, it's been years since I was familiar enough with everything to know how to express exactly my confusion. But if you (or anyone) wants to take one more crack, I will appreciate it :)
- bee_rider 4y agoI don't think I'm able to give a real crack at the "where does it come from" question, but an example that might be intuitive -- if you had a system of equations, like high school algebra stuff: a w + b v = y c w + d v = z If you know w and v, and want y and z, this is equivalent to a matrix multiplication: [a b] [v] = [y] [c d] [w] [z] And if you are solving that classic highschool problem "you know y and z, what are v and w," it is equivalent to the linear system solve operation, or multiplication by the inverse of the matrix. [v] = ([a b])^-1 [f] [w] ([c d]) [g] I apologize for the formatting. Imagine any time I've got parens or brackets on multiple lines, they are their big equivalent that envelopes both lines.