The module aims to provide sufficient knowledge of matrix theory and of the solution of systems of linear equations for use in later modules in Mathematics and Statistics, to give an understanding of the basic concepts of linear algebra, and to develop the ability to solve problems and prove theorems involving these concepts.
1. System of linear equations (1.1 Use Gaussian elimination on systems linear equations. Determine the existence of solutions. Compute parametrised solutions.)
2. Vectors (2.1 Vectors in R2,R3, Rn, and general vector spaces. linear combination, linear independence/dependence, span, spanning sets, and bases)
3. Subspaces (3.1 Rank and nullity, Linear maps, Determinants, and Change of bases in the R^n and general vector spaces)
4. Inner product spaces (4.1 orthogonality, orthonormality, invertibility for Rn and general vector spaces. Gram-Schmidt algorithm. Orthogonal projections)
5. Eigenvalues (5.1 Characteristic polynomial, diagonalisability, eigenvalues, and eigenvectors)
6. Applications of Linear Algebra (6.1 Such as: Polynomial regression, powers of matrices, population dynamics, Markov chains, transition matrices, Perron-Frobenius Theorem, Pagerank Algorithm)
By the end of the course, students should be able to do the following:
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SCQF Level: 8
Credits: 15