Asking why matrix multiplication isn't just componentwise multiplication is an excellent question: in fact, componentwise multiplication is in some sense the most "natural" generalization of real multiplication …

Dot product has a specific meaning. Matrix multiplication has no specific meaning, than may be a mathematical way to solve system of linear equations Why, historically, do we multiply matrices as …

My question is intact no matter whether matrix multiplication was done this way only after it was used as representation of composition of transformations, or whether, on the contrary, matrix multiplication …

May 13, 2014 · I think this is wrong. You can't partition both of them same way. If you partition after x rows in first matrix , you've to partition after x columns (not rows ) in the second matrix. Otherwise …

5 A particular case when orthogonal matrices commute. Orthogonal matrices are used in geometric operations as rotation matrices and therefore if the rotation axes (invariant directions) of the two …

Nov 2, 2020 · If the matrices have dimensions that are multiples of each other (or close to multiples) then we can use the square algorithms and block multiplication to speed up the implementation.

Jan 11, 2018 · Matrix multiplication is associative, so you can do it in whichever order you like. You can prove it by writing the matrix multiply in summation notation each way and seeing they match.

I would like to know of how to look at or define matrix multiplication, in a manner which makes it easy (for the average student) to compute by hand, while being intuitive and consistent for use for later …

Oct 4, 2020 · Because matrix multiplication is such that it corresponds to composition of the associated linear maps, and composition of (linear) maps is not commutative.

May 15, 2025 · Applying recursively Strassen's algorithm on $4\\times4$ matrices results in $49$ elementary multiplications. Are there methods tailored for $4\\times4$ matrices which can do better? …