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]
  • Elementary Row Operations
    tl;dr: Vector Operation, Matrix Multiplication, Elementary Row Operations, Elementary Matrices
    [slides] [RowReduce-Haffman]
  • Echelon Forms and Row Reduction
    tl;dr: Row Reduced Matrix, Echelon Form, RREF, Solution of Linear System, Geometric Interpretation
    [slides] [LinearEquation-David_C_Lay]
  • Vector Space
    tl;dr: Field, Vector Space, Linear Combination, Span-Linear Hull
    [slides] [VectorSpace-Axler]
  • Subspace
    tl;dr: Subspace And Intersection, Sum, Direct Sum And Union On Subspaces, Span And Subspace
    [slides] [Subspace-Haffman] [video]
  • Linear Independence
    tl;dr: Linear Independence, Functions Linearly Independent, Polynomials Linearly Independent
    [slides] [video]
  • Bases and Dimension
    tl;dr: Basis, Dimension, Finite Dimensional Subspace, Coordinates
    [slides]
  • Matrix Rank
    tl;dr: Row & Column Spaces, Null Space, Nullity, Rank, Four Fundamental Subspaces
    [slides] [video]
  • Inner Space Product
    tl;dr: Linear Form, Bilinear Form on Real & Complex Vector Space, Inner Product, Inner Product Space
    [slides] [video]
  • Euclidian Norm, Inequalities and Angle
    tl;dr: Inequalities, Euclidean Norm, Euclidean Metric (Distance), & Angle
    [slides]
  • Orthogonality
    tl;dr: Orthogonality, Gram–Schmidt Algorithm, Orthogonal Complements, Projection
    [slides]
  • Linear Transformation
    tl;dr: Linear Transformation (Linear Map), Rotation-Projection-Reflection, Non-linear Maps, Null space and Range, Onto and One-to-One Linear Transformation, Fundamental Theorem of Linear Maps
    [slides] [Intuition1] [Intuition2]
  • Change of Basis
    tl;dr: Invertible Linear Maps, Basis Review, Change of Basis, L(V) and Change of Basis, L(V,W) and Change of Basis
    [slides] [video]
  • Inverse Matrix
    tl;dr: Left Inverse, Right Inverse, Square Matrix Inverse
    [slides]
  • Determinant
    tl;dr: Multilinear Form, Determinant Of Matrix, Properties Of Determinant
    [slides]