Linear Algebra & Statistics

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The following courses are prerequisites:

This unit is offered as a part of the following awards:

Investigate the theory of matrices, concentrating on eigenvalues and eigenvectors, crafting sustained mathematical argument with proofs when necessary.
Identify foundations for probability and statistics, with the ability to make statistical decisions and apply appropriate statistical tests.
Calculate linear transformations and their matrices, change of basis and isomorphisms.
Analyse the set theory foundations for probability and statistics.
Recognise eigenvalues, eigenvectors and their applications.
Calculate linear transformations and their matrices, change of basis and isomorphisms.
Analyse the set theory foundations for probability and statistics.

Eigenvalues and Eigenvectors: Introduction to eigenvalues and eigenvectors, Diagonalisation, Orthogonal matrices, Orthogonal diagonalisation, Complex vector spaces.
Applications of eigenvalues and eigenvectors: Dynamical systems, applications to differential equations, Markov chains
Matrices: Cauchy Schwartz inequality, Gram Schmidt orthogonalisation.
Linear transformations: Linear transformations in R2, General linear transformations, Change of basis, Kernel and Range, Compositions and Inverse, Isomorphisms, Matrices for linear transformations
Statistics and Probability: Sample descriptives and Numerical summaries, Probability concepts – events, sets, independence, Conditional probability, Density functions, Moment generating functions, Normal distribution, Special distributions - Binomial, Poisson, Gamma, Uniform, Exponential, Chi-squared, Central Limit Theorem.
Statistical Decisions: Tests for means and proportions, Hypothesis testing and significance levels, Confidence intervals, Two sample tests, Bivariate experiments, Chi-squared tests, Linear regression, Correlation analysis

NOTE: The statistics sections 5 & 6 must be allocated at least half of the available time.