To multiply two matrices is the same thing as composing the corresponding linear transformations (or linear maps). The following is covered in a text on linear algebra (such as Hoffman-Kunze):

Dec 19, 2020 · The sum of matrices corresponds to the transformation which is the sum of the two given transformations. Addition of linear transformations require the domain and range to be identical. The …

Feb 20, 2017 · I'm studying linear algebra using the online MIT course, and in the third lecture, the professor showed us 5 ways to multiply matrices, they can be found here: MIT Linear Algebra, …

Jan 30, 2025 · To answer your question how my Problem is different to the proposed problem you linked: I completely understood, why we calculate rows by columns, but I wonder, if there is any …

Dec 6, 2022 · I'd like to step thru the algorithm below to see if I understand how it works. MATRIX-MULTIPLY-RECURSIVE(A, B, C, n) if n == 1 // Base case. c_11 = c_11 + a_11 · b_11 return //

May 15, 2025 · 2 Yes — AlphaEvolve, an automated coding agent from Google DeepMind, has recently discovered an algorithm to multiply two $4\times 4$ complex-valued matrices using only $48$ scalar …

Sep 29, 2020 · Because, as you say in your question, you can multiply two matrices only when the number of rows in the first matrix is equal to the number of columns in the second matrix. This shows …

Dec 18, 2016 · You say you know how to multiply matrices, so take a look at one specific element in the product $C=AB$, namely the element on position $ (i,j)$, i.e. in the $i$ th row and $j$ th column.

64 Is it possible to multiply A [m,n,k] by B [p,q,r]? Does the regular matrix product have generalized form? I would appreciate it if you could help me to find out some tutorials online or mathematical …

Why is it "not intuitive"? If you ask someone how to multiply two matrices and they think about what that multiplication is supposed to mean, they absolutely will come up with the usual definition.