Jan 15, 2026 · An inner product gives a vector space a Euclidean geometry, and there are actually lots of inner products that can give an abstract real or complex vector space a Euclidean geometry. The …

Matrix multiplication notation Ask Question Asked 9 years, 2 months ago Modified 4 years, 10 months ago

Nov 6, 2015 · In my math lectures, we talked about the Gram-Determinant where a matrix times its transpose are multiplied together. Is $A A^\\mathrm T$ something special for any ...

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.

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...

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, …

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.

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 …

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 …

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 …