Matrix Multiplication

matrix multiplication represents a topic that has garnered significant attention and interest. Matrix multiplication notation - Mathematics Stack Exchange. Matrix multiplication notation Ask Question Asked 8 years, 11 months ago Modified 4 years, 7 months ago linear algebra - Dot product vs Matrix multiplication, is the later a .... 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 multiplication is a tool to find vector dot product (assuming we are talking about matrices in the context of vectors)

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 while multiplying you'll have to multiply mn block with another mn block which is not possible.

In relation to this, (you need np block) Try it with your example. linear algebra - When is matrix multiplication commutative .... You'll need to complete a few actions and gain 15 reputation points before being able to upvote.

Upvoting indicates when questions and answers are useful. What's reputation and how do I get it? Instead, you can save this post to reference later. Practical uses of matrix multiplication - Mathematics Stack Exchange.

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 walks betw... Moreover, linear algebra - Proving Distributivity of Matrix Multiplication ....

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 is really just distributivity of composition of linear transformations, which lends itself to a far more transparent proof: Fast(est) and intuitive ways to look at matrix multiplication?.

The problem I have is doing matrix multiplication quickly by hand, particularly when the A A is p × 1 p × 1 and B B is 1 × q 1 × q. 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 proofs. Not understanding derivative of a matrix-matrix product.. I am trying to figure out a the derivative of a matrix-matrix multiplication, but to no avail.

This document seems to show me the answer, but I am having a hard time parsing it and understanding it... This perspective suggests that, how to write the derivative of a matrix product with respect to a matrix?. In the same way that the Jacobian matrix of a function $g : \mathbb R^n \to \mathbb R^m$ gives you an $m \times n$-matrix, the Jacobian matrix of the function $f$ gives us an $ (np^2m) \times nm$ matrix, something quite discouraging. To enlighten us, we use the fact that our function $f$ is quadratic in the coefficients of $X$ and $Y$.