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]
  • Eigenvalue - Eigenvector
    tl;dr: Eigenvalue, Eigenvector, and Characteristic Polynomial
    [slides] [video1] [video2]
  • Diagonalization
    tl;dr: Similarity, Eigenvalue Multiplicity, and Diagonalization
    [slides] [video1] [video2] [video3]
  • Orthogonality
    tl;dr: Orthogonality, Gram-Schmidt Algorithm, Orothogonal Complements
    [slides]
  • Symmetric Matrices and Quadratic Forms
    tl;dr: Symmetric Matrix, Quadratic Form, Positive Definite Tests, Gram Matrix
    [slides]
  • Matrix Factorization
    tl;dr: Eigenvalue, Eigenvector, and Characteristic Polynomial
    [slides] [video]
  • Singular Values and Singular Vectors
    tl;dr: Eigenvalue, Eigenvector, and Characteristic Polynomial
    [slides] [video]
  • SVD
    tl;dr: Eigenvalue, Eigenvector, and Characteristic Polynomial
    [slides] [video]
  • Inner Product Space
    tl;dr: Linear Form, Bilinear Form on Real & Complex Vector Space, Inner Product, Inner Product Space
    [slides] [video]
  • Euclidian Norm, Euclidian Distance, & Angle
    tl;dr: Inequalities, Euclidean Norm, Euclidean Metric (Distance), & Angle
    [slides]
  • Norm Space
    tl;dr: Norm Space
    [slides] [video]
  • Derivation
    tl;dr: Derivation
    [slides] [video]