Advanced Linear Algebra Full Video Course

Linear algebra is central to almost all areas of mathematics. For instance,
#linearalgebra is fundamental in modern presentations of geometry, including for defining basic objects such as lines, planes and rotations. Also, functional analysis may be basically viewed as the application of linear algebra to spaces of functions. Linear algebra is also used in most sciences and engineering areas, because it allows modeling many natural phenomena, and efficiently computing with such models. For nonlinear systems, which cannot be modeled with linear algebra, linear algebra is often used for dealing with first-order approximations, using the fact that the differential of a multivariate function at a point is the linear map that best approximates the function near that point.
** Topics of the course **
Linear Algebra - Least Squares Approximation - 01 - Introduction (0:00)
Linear Algebra - Least Squares Approximation - 02 - Fundamental Theorem (09:12)
Linear Algebra - Least Squares Approximation - 03 - Fitting data to a straight curve Part 1 (21:17)
Linear Algebra - Least Squares Approximation - 04 - Fitting data to a straight curve Part 2 (29:27)
Linear Algebra - Least Squares Approximation - 05 - Fitting data to a straight curve Part 3 (37:40)
Linear Algebra - Least Squares Approximation - 06 - Fitting data to a straight curve example (45:01)
Linear Algebra - Least Squares Approximation - 07 - Fitting data to more general functions (51:10)
Linear Algebra - Least Squares Approximation - 08 - The inverse of A transpose times A (01:01:38)
Linear Algebra - Hamming's error correcting codes - 01 - Hamming matrices (1:13:31)
Linear Algebra - Hamming's error correcting codes - 02 - Properties of Hamming matrices (01:17:35)
Linear Algebra - Hamming's error correcting codes - 03 - Example (1:26:33)
Linear Algebra - Hamming's error correcting codes - 04 - Parity bits (1:40:36)
Topics in Linear Algebra - The Functional Calculus - 01 - Theorem and Example (1:50:47)
Topics in Linear Algebra - The Functional Calculus - 02 - Square-root of a positive matrix (1:57:32)
Topics in Linear Algebra - The Functional Calculus - 03 - Polynomial interpolation (2:04:18)
Topics in Linear Algebra - The Functional Calculus - 04 - The determinant of a Van dermonde matrix (2:13:29)
Topics in Linear Algebra - The Functional Calculus - 05 - Proof of main theorem (2:28:17)
Affine subspaces and transformations - 01 - affine combinations (2:39:22)
Affine subspaces and transformations - 02 - affine subspaces (2:49:08)
Affine subspaces and transformations - 03 - affine transformations (3:13:11)
Affine subspaces and transformations - 04 - composition of affine transformations (3:16:37)
Stochastic maps - 01 - Conditional probabilities (3:25:53)
Stochastic maps - 02 - Composing conditional probabilities (3:36:50)
Stochastic maps - 03 - Products of conditional probabilities and a.e. equivalence (3:47:38)
Stochastic maps - 04 -Bayes' theorem (3:58:37)
* Credit **
Course Created By: Prof. Arthur Parzygnat
UA-cam Channel: / @arthurparzygnat
License: Creative Commons Attribution license (reuse allowed)
** Join our community **
Join our FB Group: / cslesson
Like our FB Page: / cslesson
Website: cslesson.org

[@AcademicLesson]

⭐️ Learn more: ua-cam.com/play/PLKp3X-578hN8s5htUiN-8yO38BR4eaPsb.html
⭐️ Table of contents ⭐️
Linear Algebra - Least Squares Approximation - 01 - Introduction (0:00)
Linear Algebra - Least Squares Approximation - 02 - Fundamental Theorem (09:12)
Linear Algebra - Least Squares Approximation - 03 - Fitting data to a straight curve Part 1 (21:17)
Linear Algebra - Least Squares Approximation - 04 - Fitting data to a straight curve Part 2 (29:27)
Linear Algebra - Least Squares Approximation - 05 - Fitting data to a straight curve Part 3 (37:40)
Linear Algebra - Least Squares Approximation - 06 - Fitting data to a straight curve example (45:01)
Linear Algebra - Least Squares Approximation - 07 - Fitting data to more general functions (51:10)
Linear Algebra - Least Squares Approximation - 08 - The inverse of A transpose times A (01:01:38)
Linear Algebra - Hamming's error correcting codes - 01 - Hamming matrices (1:13:31)
Linear Algebra - Hamming's error correcting codes - 02 - Properties of Hamming matrices (01:17:35)
Linear Algebra - Hamming's error correcting codes - 03 - Example (1:26:33)
Linear Algebra - Hamming's error correcting codes - 04 - Parity bits (1:40:36)
Topics in Linear Algebra - The Functional Calculus - 01 - Theorem and Example (1:50:47)
Topics in Linear Algebra - The Functional Calculus - 02 - Square-root of a positive matrix (1:57:32)
Topics in Linear Algebra - The Functional Calculus - 03 - Polynomial interpolation (2:04:18)
Topics in Linear Algebra - The Functional Calculus - 04 - The determinant of a Van dermonde matrix (2:13:29)
Topics in Linear Algebra - The Functional Calculus - 05 - Proof of main theorem (2:28:17)
Affine subspaces and transformations - 01 - affine combinations (2:39:22)
Affine subspaces and transformations - 02 - affine subspaces (2:49:08)
Affine subspaces and transformations - 03 - affine transformations (3:13:11)
Affine subspaces and transformations - 04 - composition of affine transformations (3:16:37)
Stochastic maps - 01 - Conditional probabilities (3:25:53)
Stochastic maps - 02 - Composing conditional probabilities (3:36:50)
Stochastic maps - 03 - Products of conditional probabilities and a.e. equivalence (3:47:38)
Stochastic maps - 04 -Bayes' theorem (3:58:37)

[@Naomi-ix6tn]

Thank you for the video

[@AnkitMishra-hk4in]

Starting it on 7 September

[@theobellash6440]

How does this transparent board work?
How do you make it to write with left or right hand? Scriptures are still visible and readable correctly

[@Erik-lp2mc]

He's probably not left-handed. So I'd say he wrote normally on a transparent glass board, and they reversed the image on the Y axis

[@nashtrashcool]

Reversed the vid

[@blackumbrella6199]

I think I found the reason why Aliens quit their attempt to invade earth 😐

[@ankitnmnaik229]

What? Cause of our math?

[@allaandra3055]

It's a bit annoying to have to download and speed up the video by a factor of 3 to make him speak at a normal pace....

[@stzsun]

are you writing in reverse wow

[@Ryan-le2im]

I was blown away the second the video started

[@prashantchauhan8010]

he is writing with his right hand on a glass screen and the video is projection is reversed. this is how glass board lectures are made

[@Ryan-le2im]

@@prashantchauhan8010 ah good to know :)