PMAT 21553: Linear Algebra

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Course code  :  PMAT 21553

Title               :  Linear Algebra

Pre-requisites :  PMAT 11522

 Learning outcomes:

Upon successful completion of the course students should be able to

  • recognize vector spaces and subspaces, linear transformations and eigenspaces of matrices
  • recognize the concepts of the terms span, linear independence, basis, and dimension, and apply these concepts to various vector spaces and subspaces
  • use the definition and properties of linear transformations and matrices of linear transformations and change of basis, including kernel, range and isomorphism
  • compute with the characteristic polynomial, eigenvectors, eigenvalues and eigenspaces, as well as the geometric and the algebraic multiplicities of an eigenvalue and apply the basic diagonalization result
  • compute inner products and determine orthogonality on vector spaces, including Gram-Schmidt orthogonalization
  • apply orthogonal decomposition of inner product spaces

 Course Contents:

Vector Spaces: Vector Spaces, Subspaces, Spanning sets and Linear Independence, Basis and dimension, Coordinates, Change of Basis and Transition matrix, Similarity, Dimensional Theorem.

Linear transformations: Kernel and Range of Linear Transformation, Rank and Nullity Theorem. Isomorphisms, Standard Matrix, Applications of Linear Transformation

Eigenvalues and Eigenvectors: Eigenvalues and eigenvectors, Eigen spaces, Diagonalization, Inner product, Gram-Schmidt orthogonalization process, Orthogonal complement, Orthogonal  projections, Characteristic polynomial, Cayley-Hamilton,Minimum polynomial.

 Method of Teaching and Learning: A combination of lectures and tutorial discussions.

 Assessment: Based on tutorials, tests and end of course examination.

 Recommended readings:

  1. Larson, R. and Falvo, D.C., (8th edition, 2016) Elementary Linear Algebra, Brooks Cole.
  2. Andrilli, S. and Hecker, D., (3rd edition, 2016) Elementary Linear Algebra, Elsevier Science.
  3. DeFranza, J. and Gagliardi, D., (2015) Introduction to Linear Algebra with Applications, Waveland Press.


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