Courses :: Module, LINEAR ALGEBRA 2 (A)

	Overview
	Module Objective: To introduce students to coordinate geometry in n-dimensions, vector spaces, linear transformations, eigenvalues and applications of linear algebra. Definition of n x n determinant via permutations, determinants via expansion along a row or along a column, determinants via Gaussian elimination; inverses of n x n matrix via row reduction, mention adjoint formula and Cramer's rule. Coordinate geometry and vectors in n-dimensions; norm, distance, dot product; triangle and parallelogram laws; angle, triangle and Cauchy-Schwartz inequalities; cross and triple product, volume of a parallelopiped. Vector spaces with a focus on real vector spaces; linear span, linear independence, basis and dimension; linear maps and matrices; matrix multiplication as composition of linear maps; rank and nullity; rotations, reflections and orthogonal projections in 3 dimensions; Eigenvalues and eigenvectors of a matrix, diagonalization. Applications, for example computer graphics, ranking in search engines, linear regression, Markov processes, Quantum systems. Computation using mathematical computing software.

Overview

Module Objective:
To introduce students to coordinate geometry in n-dimensions, vector spaces, linear transformations, eigenvalues and applications of linear algebra.

Definition of n x n determinant via permutations, determinants via expansion along a row or along a column, determinants via Gaussian elimination; inverses of n x n matrix via row reduction, mention adjoint formula and Cramer's rule.

Coordinate geometry and vectors in n-dimensions; norm, distance, dot product; triangle and parallelogram laws; angle, triangle and Cauchy-Schwartz inequalities; cross and triple product, volume of a parallelopiped.

Vector spaces with a focus on real vector spaces; linear span, linear independence, basis and dimension; linear maps and matrices; matrix multiplication as composition of linear maps; rank and nullity; rotations, reflections and orthogonal projections in 3 dimensions; Eigenvalues and eigenvectors of a matrix, diagonalization.

Applications, for example computer graphics, ranking in search engines, linear regression, Markov processes, Quantum systems. Computation using mathematical computing software.

	Learning Outcomes
	On successful completion of the module, students should be able to: Understand the role of determinants in linear algebra. Compute the determinant of a matrix. Invert a matrix and solve matrix equations using inverses. Find a basis and the dimension of a vector space. State and prove results about vector spaces and subspaces. Find a matrix of a linear map. Use matrix multiplication to compose linear transformations. Compute the rank and nullity of a matrix. Obtain the eigenvalues and eigenvectors of an n x n matrix. Have some appreciation for abstract algebra. State relevant definitions and theorems.

Learning Outcomes

	Autumn Supplementals/Resits
	Are supplemental/resit registrations permitted? Yes Continuous assessment mark is carried forward to the Autumn. University scheduled written examination (Autumn): 120 minutes, On-campus

Autumn Supplementals/Resits

	Pre-Requisites
	MT112A or equivalent

Pre-Requisites

Search form

Courses / Module

LINEAR ALGEBRA 2 (A)

Semester 1

Semester 2