Dive into a comprehensive 4-hour video course on advanced linear algebra, exploring its fundamental role in mathematics, sciences, and engineering. Master least squares approximation, including data fitting and the inverse of transpose matrices. Delve into Hamming's error-correcting codes, examining Hamming matrices and parity bits. Explore the functional calculus, covering topics like polynomial interpolation and Van der Monde matrix determinants. Study affine subspaces and transformations, understanding combinations, subspaces, and compositions. Conclude with an in-depth look at stochastic maps, conditional probabilities, and Bayes' theorem. Enhance your understanding of this crucial mathematical field through lectures by Prof. Arthur Parzygnat, designed to equip you with advanced linear algebra concepts and applications.
Overview
Syllabus
Linear Algebra - Least Squares Approximation - 01 - Introduction
Linear Algebra - Least Squares Approximation - 02 - Fundamental Theorem
Linear Algebra - Least Squares Approximation - 03 - Fitting data to a straight curve Part 1
Linear Algebra - Least Squares Approximation - 04 - Fitting data to a straight curve Part 2
Linear Algebra - Least Squares Approximation - 05 - Fitting data to a straight curve Part 3
Linear Algebra - Least Squares Approximation - 06 - Fitting data to a straight curve example
Linear Algebra - Least Squares Approximation - 07 - Fitting data to more general functions
Linear Algebra - Least Squares Approximation - 08 - The inverse of A transpose times A
Linear Algebra - Hamming's error correcting codes - 01 - Hamming matrices
Linear Algebra - Hamming's error correcting codes - 02 - Properties of Hamming matrices
Linear Algebra - Hamming's error correcting codes - 03 - Example
Linear Algebra - Hamming's error correcting codes - 04 - Parity bits
Topics in Linear Algebra - The Functional Calculus - 01 - Theorem and Example
Topics in Linear Algebra - The Functional Calculus - 02 - Square-root of a positive matrix
Topics in Linear Algebra - The Functional Calculus - 03 - Polynomial interpolation
Topics in Linear Algebra - The Functional Calculus - 04 - The determinant of a Van dermonde matrix
Topics in Linear Algebra - The Functional Calculus - 05 - Proof of main theorem
Affine subspaces and transformations - 01 - affine combinations
Affine subspaces and transformations - 02 - affine subspaces
Affine subspaces and transformations - 03 - affine transformations
Affine subspaces and transformations - 04 - composition of affine transformations
Stochastic maps - 01 - Conditional probabilities
Stochastic maps - 02 - Composing conditional probabilities
Stochastic maps - 03 - Products of conditional probabilities and a.e. equivalence
Stochastic maps - 04 -Bayes' theorem
Taught by
Academic Lesson
