Linear algebra
Not offered in 1997
Dr David Wilson
3 points * First semester * 2 hours per week * Gippsland/Distance (even numbered years only) * Prerequisites: GAS1612 * Corequisite: GAS2614 is desirable * Prohibition: MAT2020
Objectives The objectives of this subject are for students to understand the basic properties of vector spaces; determine whether a given subset of a vector space is also a vector space; determine the matrix representation of a linear transformation on a finite dimensional vector space; compute non-Euclidean inner products; find the orthogonal projection of a vector onto a subspace; find the least squares approximation of a continuous function by an n-th degree polynomial; use the Gram-Schmidt process to construct an orthonormal basis; find the eigenvalues and eigenvectors of linear operators; diagonalise symmetric matrices associated with quadratic forms, and apply this to the study of quadric surfaces; use the power method to approximate the dominant eigenvector of a square matrix, determine the corresponding eigenvalue, using the Rayleigh quotient; reduce a symmetric matrix to a tri-diagonal form, using Householder transformations, and find its eigenvalues.
Synopsis This subject aims to continue the study of linear algebra beyond first-year level, emphasising the general concepts of a vector space and the particular case of an inner product space as unifying threads in mathematics. Euclidean and general vector spaces: general concepts, basis and dimension, linear transformations, inner product spaces; orthogonalisation and projection; matrix algebra: diagonalisation theorems for real symmetric matrices, quadratic forms, applications to analytical geometry, numerical methods of eigenvalue analysis for real symmetric matrices.
Assessment Assignments: 40% * Examination: 60%
Prescribed texts
Anton H Elementary linear algebra Applications version, 7th edn, Wiley, 1994
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