**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****:**

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