Linear Algebra Tutorial by PhD in AIㅣ2-hour Full Course

2-hour Full Lecture on Linear Algebra for AI (w/ Higher Voice Quality)

🤖Welcome to our Linear Algebra for Beginners tutorial!

This tutorial is designed for both linear algebra beginners and AI enthusiasts.

We finally returned with a 2-hour full lecture of "Linear Algebra Tutorial for AI"! In this lecture, we cover various topics in Linear Algebra from basic matrix operations to their application to AI.

Starting this week, a new series of statistics tutorials will be released on our YouTube channel, MetaCode. Be sure to show your support by liking this video and subscribing to our channel!

🧾Contents:
00:00:00 Intro
00:02:37 Fundamental Concepts of Linear Algebra
00:03:46 Dimension of Data
00:16:18 Linear Independence
00:25:30 Rank of a Matrix
00:31:45 Null Space
00:41:14 Matrix as Linear Operator
00:48:18 Rotation Matrix I
00:51:11 Matrix Multiplication
00:53:52 Key Notations
00:55:33 Matrix Multiplication in Neural Networks
01:00:29 Rotation Matrix II
01:04:47 Determinant of 2x2 Matrix
01:10:28 Determinant of 3x3 Matrix
01:14:00 Zero Determinant
01:17:25 Inverse Matrix
01:22:25 Dot Product
01:29:30 Dot Product in Attention Mechanism
01:32:45 Review (Rank, Null-Space, Determinant, Inverse)
01:34:07 Cross Product
01:36:43 Eigenvectors & Eigenvalues
01:49:07 Useful Formulas
01:49:25 Matrix Diagonalization
01:52:57 Principal Component Analysis (PCA)
01:59:18 Matrix Exponentials
02:01:20 Solution of Linear Systems
02:02:37 Pseudo-Inverse Matrix
02:05:00 Review

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