Courses Detail Information

MATH2140J – Linear Algebra


OLGA DANILKINA;Jing Liu;Manuel Charlemagne

Credits: 4 Credits. No credit granted to those who have completed or are enrolled in Vv417.



An introduction to the main concepts of linear algebra: matrix operations, echelon form, solution of systems of linear equations, Euclidean vector spaces, linear combinations, independence and spans of sets of vectors in Euclidean space, eigenvectors and eigenvalues, similarity theory. There are applications to discrete Markov processes, linear programming, and solutions of linear differential equations with constant coefficients.

Course Topics:

  1. Introduction: systems of linear equations, Gauss-Jordan elimination, reduced row-echelon form, matrix rank matrices, number fields, Abelian groups, linear spaces, linear independence, basis(10 hrs at 45 min each)
  2. Linear operators, linear transformations in Euclidean spaces, inverses, image and kernel of a linear operator, coordinates, isomorphism. (10 hrs)
  3. Inner product spaces, orthogonality, least-squares approximations (8 hrs)
  4. Determinants (4 hrs)
  5. Dynamical systems and eigenvectors, diagonalization, Markov chains and Perron – Frobenius theorem, Cayley-Hamilton theorem, spectral theorem, introduction into spectral graph theory, quadratic forms, SVD and low-rank approximations(18 hrs)
  6. Applications of linear algebra to certain problems in combinatorics. (4 hrs)
  7. Three exams (6 hrs)