Course

MATH-115(a): Advanced linear algebra II - diagonalization

Summary

L'objectif du cours est d'introduire les notions de base de l'algèbre linéaire et de démontrer rigoureusement les résultats principaux de ce sujet.

Lectures

Instructor

Friedrich Eisenbrand

Friedrich Eisenbrand's main research interests lie in the field of discrete optimization, in particular in algorithms and complexity, integer programming, geometry of numbers, and applied optimization. He is best known for his work on efficient algorithms for integer programming in fixed dimension and the theory of cutting planes, which are an important tool to solve large scale industrial optimization problems in practice. Before joining EPFL in March 2008, Friedrich Eisenbrand was a full professor of mathematics at the University of Paderborn. Friedrich received the Heinz Maier-Leibnitz award of the German Research Foundation (DFG) in 2004 and the Otto Hahn medal of the Max Planck Society in 2001.

Official source

https://edu.epfl.ch/coursebook/en/advanced-linear-algebra-ii-diagonalization-MATH-115-A

Moodle Page

http://go.epfl.ch/MATH-115_a

About this result

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Summary

L'objectif du cours est d'introduire les notions de base de l'algèbre linéaire et de démontrer rigoureusement les résultats principaux de ce sujet.

Lectures

Instructor

Friedrich Eisenbrand

Official source

https://edu.epfl.ch/coursebook/en/advanced-linear-algebra-ii-diagonalization-MATH-115-A

Moodle Page

http://go.epfl.ch/MATH-115_a

About this result

Ontological neighbourhood

Mathematics

Algebra: Linear algebra

Lectures in this course (24)

Symmetric Matrices: Eigenvalues and Diagonalization

Covers symmetric matrices, eigenvalues, and diagonalization process for spectral theorem applications.

Positive Definite Matrices

Covers positive definite matrices and their properties, focusing on strict positivity of principal minors.

Spectral Theorem: Min-Max Criterion

Explores the Spectral Theorem, emphasizing the Min-Max Criterion for symmetric matrices and the properties of positive definite matrices.

Singular Value Decomposition, Pseudoinverse

Covers Singular Value Decomposition and Pseudoinverse, explaining their applications in data compression and linear systems.

Best approximative subspace

Explores finding the minimal solution of a problem using orthogonal bases and factorization, emphasizing uniqueness and practical examples.

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