You can download the lectures here. We will try to upload lectures prior to their corresponding classes.

  • Introduction
    tl;dr: Course's Policies and Introduction to Syllabus
    [slides]
  • Vector Space
    tl;dr: Field, Vector Space, Linear Combination, Span-Linear Hull
    [slides] [VectorSpace-Axler]
  • Subspace
    tl;dr: Subspace, Intersection and Union, Span, Sum and Direct Sum of Subspaces
    [slides] [Subspace-Haffman] [video]
  • Elementary Row Operations
    tl;dr: Vector Operations, Matrix Multiplication, Elementary Row Operations, Elementary Matrices, and Linear Equation
    [slides] [RowReduce-Haffman]
  • Echelon Forms and Row Reduction
    tl;dr: Row Reduced Matrix, Echelon Form, RREF, and Solutions of a Linear System
    [slides] [LinearEquation-David_C_Lay]
  • Linear Independence
    tl;dr: Linear Independence, Linear Independent Functions and Polynomials
    [slides] [video]
  • Bases and Dimension
    tl;dr: Basis, Finite Dimensional Subspace, Dimension, and Coordinates
    [slides]
  • Matrix Rank
    tl;dr: Row and Columns Space, Null Space, Nullity, and Rank
    [slides] [video]
  • Linear Transformation
    tl;dr: Linear Map, Rotation, Projection, Reflection, Non-Linear Maps, Onto and One-to-One Transformation, Fundamental Theorem of Linear Maps, Invertible Linear Maps, and Isomorphic
    [slides] [Intuition1] [Intuition2]
  • Change of Basis
    tl;dr: Invertible Linear Maps, and Change of Basis
    [slides] [video]
  • Inverse
    tl;dr: Left, Right, and Square Matrix Inverse
    [slides]
  • Determinant
    tl;dr: Linear Form, Bilinear Form, Multilinear Form, Matrix Determinant, Cramer's Rule, and Determinant Properties
    [slides] [compressed]