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Linear Algebra:


Linear Equations

  • Systems of Linear Equations
  • Row Reduction and Echelon Forms
  • Vector Equations
  • The Matrix Equation Ax=b
  • Solution Sets of Linear Systems
  • Linear Independence
  • Linear Transformations and the Matrix of a Linear Transformation
  • Applications of Linear Systems and Linear Models in Business, Science and Engineering


Matrix Algebra

  • Matrix Operations and Determinants
  • The Inverse of a Matrix
  • Characterizations of Invertible Matrices
  • Partitioned Matrices
  • Matrix Factorization (LU Decomposition)
  • Applications to Computer Graphics



  •  Properties to Determinants
  • Cramer’s Rule, Volume, and Linear Transformations


Vector Spaces 

  • Vector Spaces and Subspaces
  • Null Spaces, Column Spaces, Row Spaces and Linear Transformations
  • Linearly Independent Sets; Bases
  • Coordinate Systems
  • The Dimension of a Vector Space
  • Rank
  • Change of Basis
  • Applications to Markov Chains


Eigenvalues and Eigenvectors

  • Eigenvectors and Eigenvalues
  • The Characteristic Equation
  • Diagonolization
  • Eigenvectors and Linear Transformations
  • Complex Eigenvalues


Orthogonality and Least Squares

  •  Inner Product, Length, and Orthogonality
  • Orthogonal Sets
  • Orthogonal Projections
  • The Gram-Schmidt Process and QR Factorization
  • Least-Squares Problems
  • Applications to Linear Models (Line of Regressions)
  • Inner Product Spaces


Symmetric Matrices and Quadratic Forms

  • Diagonalization of Symmetric Matrices
  • Quadratic Forms

Complex Numbers:


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