/explore
|
You are here 
|
rjlipton.com | ||
| | | | |
nickhar.wordpress.com
|
|
| | | | | 1. Low-rank approximation of matrices Let $latex {A}&fg=000000$ be an arbitrary $latex {n \times m}&fg=000000$ matrix. We assume $latex {n \leq m}&fg=000000$. We consider the problem of approximating $latex {A}&fg=000000$ by a low-rank matrix. For example, we could seek to find a rank $latex {s}&fg=000000$ matrix $latex {B}&fg=000000$ minimizing $latex { \lVert A - B... | |
| | | | |
terrytao.wordpress.com
|
|
| | | | | Let $latex {A, B}&fg=000000$ be two Hermitian $latex {n \times n}&fg=000000$ matrices. When $latex {A}&fg=000000$ and $latex {B}&fg=000000$ commute, we have the identity $latex \dis... | |
| | | | |
mattbaker.blog
|
|
| | | | | In honor of Pi Day 2023, I'd like to discuss Hilbert's 7th Problem, which in an oversimplified (and rather vague) form asks: under what circumstances can a transcendental function take algebraic values at algebraic points? The connection with $latex \pi$ is that Lindemann proved in 1882 that the transcendental function $latex f(z) = e^z$ takes... | |
| | | | |
www.johnmyleswhite.com
|
|
| | | Lately, I've been running a series of fMRI experiments on visual perception. In the interests of understanding the underlying properties of the images I'm using as stimuli, I've been trying to learn more about the matrix transformations commonly used for image compression and image manipulation. Thankfully, R provides simple-to-use implementations for all of the matrix operations I wanted to play around with, so it's been quite easy to get started. For the next few posts, I thought that I'd review the st... | ||
