This course on Advanced Linear Algebra aims to teach learners the applications of linear algebra in various fields such as geometry, functional analysis, sciences, and engineering. The course covers topics like least squares approximation, Hamming's error correcting codes, the functional calculus, affine subspaces and transformations, and stochastic maps. By the end of the course, students will have acquired skills in fitting data, understanding error correcting codes, working with matrices, and applying linear algebra concepts to real-world scenarios. The teaching method involves video lectures with a duration of 4 hours and 9 minutes. This course is intended for individuals interested in deepening their understanding of linear algebra and its practical implications across different disciplines.
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
