Linear Algebra

If you need help with any of the topics, check out PatrickJMT on Youtube. He has some of the best math videos on the internet.

Preliminary - a great article about why linear algebra is useful and important.

• Introduction
  • Linear Equations
  • Matrix notation
  • Reducing a matrix
  • Vectors
• Solution sets of linear systems
  • Homogeneous linear systems
  • Parametric vector form
  • Linear independence
• Linear transformations
• Matrix operations
  • Sums and scalar multiples
  • Powers of a matrix
  • Transpose of a matrix
  • Inverse of a matrix
  • Elementary matrices
• Applications to computer graphics
  • Homogeneous coordinates
    • 2D
    • 3D
  • Composite transformations
  • Perspective projections
• Vector spaces
  • Column space and null space of a matrix
  • Basis for a subspace
  • Coordinates
  • Dimension of a subspace
• Eigenvectors & eigenvalues
  • Determinant
  • Similarity
  • Diagonalization
• Orthogonality & least squares
  • Inner (dot) product & uses
    • Length of a vector
    • Distance between vectors
  • Orthogonal complement
  • Orthogonal sets
  • Orthogonal projections
    • Orthogonal decomposition
    • Best approximation
    • When basis for W is an orthonormal set
  • Gram-Schmidt process
    • QR factorization
  • Least-squares problems
• Symmetric matrices
  • Diagonalization of symmetric matrices
  • Singular value decomposition