Most of the time I see matrix multiplication presented and defined, as a seemingly arbitrary sequence of operations. For example, the textbook I'm currently reading for a linear algebra course defi...

Which if we write in matrix form, we need to mathematically take the transpose of a vector and do 'matrix' multiplication to get the above dot product. So coming back full circle to the question - matrix …

Dec 18, 2016 · Matrix multiplication notation Ask Question Asked 9 years ago Modified 4 years, 9 months ago

Multiplication of blocks will give diagonal $\lambda_1\lambda_2$, first off-diagonal $\lambda_1 + \lambda_2$ and second off-diagonal $1$ so assuming scalar multiplication and addition is …

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 …

May 13, 2014 · All multiplications conform, all sums work out, and the resulting matrix is the size you'd expect. There is nothing special about splitting in two so long as you match any column split of …

Aug 10, 2013 · So, matrix multiplication is just the image of composition of linear transformations under the identification of matrices with linear transformations. In particular, then, distributivity of matrix …

May 28, 2011 · Usually, the use of matrix multiplication is initially given with graphics — scalings, translations, rotations, etc. Then, there are more in-depth examples such as counting the number of …

Dec 19, 2020 · Multiple sources tell me that I can't do multiplication or addition with matrix of different sizes. You can't add matrixes of different sizes as stated by @meshal.

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.