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Stat260/cs294: Spectral Graph Methods Lecture: Basic Matrix Results (1 of 3) 2.1 Some Basics
| Content Provider | Semantic Scholar |
|---|---|
| Author | Mahoney, Michael |
| Copyright Year | 2015 |
| Abstract | Today and next time, we will start with some basic results about matrices, and in particular the eigenvalues and eigenvectors of matrices, that will underlie a lot of what we will do in this class. The context is that eigenvalues and eigenvectors are complex (no pun intended, but true nonetheless) things and—in general—in many ways not so “nice.” For example, they can change arbitrarily as the coefficients of the matrix change, they may or may not exist, real matrices may have complex eigenvectors and eigenvalues, a matrix may or may not have a full set of n eigenvectors, etc. Given those and related instabilities, it is an initial challenge is to understand what we can determine from the spectra of a matrix. As it turns out, for many matrices, and in particular many matrices that underlie spectral graph methods, the situation is much nicer; and, in addition, in some cases they can be related to even nicer things like random walks and diffusions. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://www.stat.berkeley.edu/~mmahoney/s15-stat260-cs294/Lectures/lecture02-27jan15.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
