University of Colorado Boulder - Essential Linear Algebra for Data Science 

Introduction to the Course

Linear System and Definition

Three Solution Options and Coordinate System Visualization

Linear System -> Matrix (Coefficient and Augmented)

Rules of G.E. and Solving a Linear System

G.E. Intuition and Simple Example

G.E Example - Single Solution Part 1

G.E Example - Single Solution Part 2

G.E Example - Single Solution Part 3 + Meaning

G.E. Example - Infinite Solutions

G.E. Example - No Solutions

G.E. Advanced Example - Part 1

G.E. Advanced Example - Part 2

Practice - Linear System -> Matrix Format

LS -> Matrix + G.E. Full Question Quiz

Matrix Algebra Sum

Matrix Algebra Scale + Identity Overview

Matrix Multiplication + Small Example

Matrix Multiplication - General Rules

Matrix Multiplication Example

Identity Matrix + Example

Quiz on Matrix Algebra Sum + Scale

Matrix Multiplication

Introduction to Vectors + Coordinates

Introduction to Linear Combinations

Linear Combinations

Linear Combinations Example

Span

Span Example

Ax = b

Linear Independence

Linear Independence Example Part 1

Linear Independence Example Part 2

Columns of a Matrix Being Linearly Independent

Linear Transformations

Linear Transformations Example

Matrix Inverse

Matrix Inverse Example

Why do we use matrices and vectors and not just one?

Quiz on Linear Independence

Quiz on Transformations and Inverse

Determinant Intro and 2x2 Example

Inverse of 2x2 Matrix - Quick Method

Determinant of 3x3 Matrix - Overview

Determinant of 3x3 Matrix - Example with 1st Row

Determinant of 3x3 Matrix - Example with 2nd Row

Eigenvalue and Eigenvector - Overview

Finding Eigenvector if Given Eigenvalue

Characteristic Polynomic - Finding Eigenvalues

Find the Determinant of a 2x2 Matrix

Find Eigenvalue then Eigenvector of a Matrix (2x2)

Find Eigenvalue then Eigenvector of a Matrix (3x3)

Transpose and Inner (Dot) Product

Norm (Length) of a Vector

Unit Vector Creation

Distance Between Two Vectors

Orthogonal Vectors

Orthogonal Projections Part I

Orthogonal Projections Part II

Least Squares Overview

Least Squares Example

Important Final Concepts

Finding Least Squares Solutions

Final Exam