Lecture

Coxeter Groups: Spectral Theorem and Sylvester's Criterion

Description

This lecture covers the Sylvester criterion for positive definite matrices and a recursive formula for the determinant of a marked graph. It explores the classification of connected positive definite Coxeter graphs, the spectral theorem for real symmetric matrices, and the properties of eigenvalues. The lecture also delves into the concept of Coxeter graphs, their principal minors, and subgraphs. Additionally, it discusses the Lemma related to the number of possible eigenvalues of a matrix based on the positivity of inner products. The lecture concludes with examples of positive definite Coxeter graphs and their determinants, emphasizing the application of the spectral theorem and Sylvester's criterion.

About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Graph Chatbot

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.