/explore
|
You are here 
|
chessapig.github.io | ||
| | | | |
francisbach.com
|
|
| | | | | [AI summary] This mathematical post explores the geometry of positive semi-definite matrices using the von Neumann entropy and related Bregman divergences to derive concentration inequalities for random matrices. | |
| | | | |
djalil.chafai.net
|
|
| | | | | Let $X$ be an $n\times n$ complex matrix. The eigenvalues $\lambda_1(X), \ldots, \lambda_n(X)$ of $X$ are the roots in $\mathbb{C}$ of its characteristic polynomial. We label them in such a way that $\displaystyle |\lambda_1(X)|\geq\cdots\geq|\lambda_n(X)|$ with growing phases. The spectral radius of $X$ is $\rho(X):=|\lambda_1(X)|$. The singular values $\displaystyle s_1(X)\geq\cdots\geq s_n(X)$ of $X$ are the eigenvalues of the positive semi-definite Hermitian... | |
| | | | |
www.jeremykun.com
|
|
| | | | | This proof assumes knowledge of complex analysis, specifically the notions of analytic functions and Liouville's Theorem (which we will state below). The fundamental theorem of algebra has quite a few number of proofs (enough to fill a book!). In fact, it seems a new tool in mathematics can prove its worth by being able to prove the fundamental theorem in a different way. This series of proofs of the fundamental theorem also highlights how in mathematics there are many many ways to prove a single theorem... | |
| | | | |
gwhphotos2.wordpress.com
|
|
| | | Hockey stick chair Be sure to visit pull up a seat for more interesting photos, and/or to share yours. | ||
