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 16, 2018 · That is actually a lot of questions that might need thorough research for complete answers but as Lord Shark noticed, many things are explained by the linear algebra point of view …

The dimension of a vector space is the number of coordinates you need to describe a point in it. Thus, a plane in $\mathbb {R}^3$, is of dimension $2$, since each point in the plane can be described by two …

Feb 29, 2016 · I have a 5x5 matrix of values. I'm looking for a simple formula that I can use to rotate the position of the values (not the values themselves) 90 degrees within the matrix. For example, here is …

If you just rotate horizontal matrices until they're vertical, then use those methods, then rotate it back, that's totally fine. Math doesn't depend on where we physically position numbers on the page.

Of course. This is also explained by John in its answer. However this identity would be valid solely for the particular case of $2\times 2$ matrices, wouldn't it?

Dec 20, 2010 · What is the Jacobian matrix? What are its applications? What is its physical and geometrical meaning? Can someone please explain with examples?

I seemed to have thoroughly confused myself today... Long story short, the question is simple. Is matrix multiplication just a special case of the dot product of two sets of vectors when the sets of

Aug 24, 2011 · Let $A$ be the matrix $$A = \\left(\\begin{array}{cc} 41 & 12\\\\ 12 & 34 \\end{array}\\right).$$ I want to decompose it into the form of $B^2$. I tried ...

Dec 15, 2021 · The easiest way to handle this is to flatten all the horizontal boundaries - not graphically, but in the way you think about the array in the background. Then it is just a several rows of square …