How to Understand the Definition of Matrix Multiplication(Useful for Writing Proofs)

How to Understand the Definition of Matrix Multiplication(Useful for Writing Proofs). The goal of this video is to make you a little bit more comfortable with the notation involved in matrix multiplication. There is a simple example of matrix multiplication at the end of the video. I hope this helps someone.

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[adamsusel]

An exercise my prof assigned was to give us a linear transformation T in terms of the output column vector and another linear transformation U in terms of its output vector. You can then compose T of U and verify that it’s the same as if you were to multiply the corresponding matrices of T and U.

Very insightful problem.

[Singularitarian]

One might wonder why matrix multiplication is defined like this. It's to make the equation A(Bx) = Cx true for any column vector x. In other words, if you take a column vector x and multiply it first by B, then by A, it turns out that this is equivalent to just multiplying x by a certain matrix C.