PMAT 21263: Linear Algebra

Course code  :  PMAT 21263

Title              :  Linear Algebra

Pre-requisites :  PMAT 11232

 Learning outcomes:

Upon successful completion of the course students should be able to

1. demonstrate understanding of the concepts of vector space, subspace linear independence, span and basis
2. determine eigenvalues and eigenvectors and solve eigenvalue problems
3. describe algebraic and geometric multiplicities of eigenvalues and linearly independent eigenvectors
4. apply principles of matrix algebra to linear transformations
5. demonstrate an understanding of inner products and associated norms

 Course Contents:

Vector Spaces: 

• Vector Spaces, Subspaces, Spanning Sets and Linear Independence, Basis and Dimension,
  Extension Theorem, Coordinates, Change of Basis and Transition Matrix, Similarity, Dimensional Theorem.

Linear transformations: 

• Linear Transformation, Kernel and Range of Linear Transformation, Rank and Nullity
  Theorem, Isomorphisms, Matrix Representation of Linear Transformation, Applications of Linear Transformation.

Eigenvalues and Eigenvectors: 

• Characteristic Polynomial, Eigenvalues and Eigenvectors, Eigen Spaces,
  Diagonalization, Inner Product Spaces, Gram-Schmidt Orthogonalization Process, Orthogonal Complement,
  Orthogonal Projections, Cayley-Hamilton Theorem, Minimum Polynomial of Matrices of Order Three.

 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. & Falvo, D.C. (2016). Elementary Linear Algebra, Brooks Cole.
2. Andrilli, S. & Hecker, D. (2016). Elementary Linear Algebra, Elsevier Science.
3. DeFranza, J. & Gagliardi, D. (2015). Introduction to Linear Algebra with Applications, Waveland Press.
4. Lay, D.C., Lay, S.R. & McDonald, J.J. (5th Ed., 2015). Linear Algebra and Its Applications, Pearson