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

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?

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.

A matrix is a way to express a linear map between finite-dimensional vector spaces, given a choice of bases for said spaces. Since linear maps are useful, matrices are obviously useful.

In my linear algebra class, we just talked about determinants. So far I’ve been understanding the material okay, but now I’m very confused. I get that when the determinant is zero, the matrix doesn’t

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Nov 6, 2013 · Matrices are considered very important in mathematics. What are some examples of applications of matrices to real world problems that would be understandable by a layman?

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 …

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 …

How do you prove that: $$ \\begin{pmatrix} 1 & 1\\\\ 1 & 0 \\end{pmatrix}^n = \\begin{pmatrix} F_{n+1} & F_n\\\\ F_{n} & F_{n-1} \\end{pmatrix}$$