MAT188 — Linear Algebra

Course focuses on linear algebra, took this in first year of my undergrad. We used the Linear Algebra with Applications textbook by Otto Bretscher. Laboratory work was done in MATLAB.

Followed by MAT187 — Calculus II (with vector-valued functions) and MAT291 — Calculus III (with vector calculus).

Concepts covered

• Set theory
• Linear equation and row reduction
• Vector
  • Dot product
• Matrices and linear transformations
  • Transpose
  • Matrix multiplication
  • Inverse matrix
• Projection
• Determinant
• Bijectivity, surjectivity, and injectivity
• Subspace
  • Image
  • Kernel subspace
  • Rank-nullity theorem
• Linear combination
• Linear independence
• Basis
  • Change of basis
  • Matrix similarity
• Orthogonality
  • Gram-Schmidt algorithm
• Least squares
  • Linear regression
• Eigenvalue and eigenvector
• Diagonalisation
  • Markov chain
• Spectral theorem
• Singular value decomposition

MATLAB

• Kirchhoff’s laws
• Plotting
• Oscillatory systems and Hooke’s law
  • Mass-spring system

Resources

• Lecture videos from 2022