Math 346 Videos, Summaries, Problem Sets
1.1 Introduction to Linear Systems and 1.2 Matrices, Vectors, and Gauss-Jordan Elimination
Recitation: Elimination with Matrices
Strang: Elimination with Matrices (only watch first 19 minutes)
1.3 On the Solutions of Linear Systems; Matrix Algebra
3Blue1Brown: Vectors, what even are they?
Recitation: Geometry of Linear Algebra
Strang: The Geometry of Linear Equations
Solving Ax = 0 (recitation video)
Solving Ax = b (recitation video)
2.1 Introduction to Linear Transformations and Their Inverses and 2.2 Linear Transformations in Geometry
3Blue1Brown: Linear Transformations
2.2 Linear Transformation in Geometry
3D Linear Transformation (3blue1brown)
2.3 Matrix Products
2.4 Inverse Matrices
Inverse matrices, (skip) column space = image, and (skip) nullspace = kernel (3blue1brown)
Matrix Mult. and Inverse Matrix (lecture Beyer)
3.1 Image and Kernel
Inverse matrices, column space = image, and nullspace = kernel (3blue1brown)
Nonsquare matrices (3blue1brown)
Overview of Key Ideas (recitation video)
3.2 Subspaces
Linear combination, span, basis vectors (3blue1brown)
Vector Subspaces (recitation video)
Vector Subspaces (recitation video 2)
Column Space and Nullspace (lecture Strange)
Solving Ax = 0: Pivot Variables, Special Solutions (lecture Strange)
3.3 The Dimension of a Subspace
Inverse Matrix, Rank, and Nullity (3blue1brown)
Independence, Basis, and Dimension (lecture Strange)
Basis and Dimension (recitation video)
The Four Fundamental Subspaces (lecture Strange)
The Four Fundamental Subspaces (recitation)
General Solution and Particular Solution (Beyer Lecture)
3.4 Coordinates and Change of Basis
4.1 Introduction to Linear Spaces
Abstract Vector Spaces (3Blue1Brown)
5.1 Orthogonal Projections and Orthogonal Bases
Orthogonal Spaces (recitation video)
5.2 Gram Schmidt
Gram Schmidt (Gil Strang lecture)
Gram Schmidt (recitation video)
QR factorization (recitation video)
5.4 Least Squares and Data Fitting
Projection onto Subspaces (recitation video)
Least Squares (recitation video)
Chapter 6 Determinants
Determinant Formulas and Cofactors (lecture Strang)
Cramer's Rule, Inverse Matrix, and Volume (lecture Strang)
Chapter 7 Eigenvalues and Eigenvectors
Eigenvalues and Eigenvectors (3blue1brown)
Eigenvalues and Eigenvectors (lecture Strang)
Eigenvalules and Eigenvectors (recitation video)
A Quick Trick to Compute Eigenvalues (3blue1brown)
