Handbook 1996 : Faculty of Science (Volume 4 page 210)
Mathematics subject : Next:618-222 | Prev:618-211 | Search | Help
618-212 "Applied Linear Algebra" appears differently in several places - choose the one you want:
1. Mathematics, Faculty of Science (v4, p210) : Next:618-222 | Prev:618-211
Credit points: 12.0
Coordinator: Dr J J Koliha
Prerequisite: One of Mathematics 618-112, 618-122, 618-200, 618-211
Contact: 39 lectures (three a week).
Timetable: Second semester
Objectives:
On completion of this subject, students should:Comprehend:
- basic and more advanced concepts of linear algebra such as vector spaces, inner product spaces, linear transformations, diagonalization of matrices, Jordan canonical form and spectral decomposition.
Have developed:
- skills in calculating eigenvalues and eigenvectors including iterative methods;
- skills in the diagonalization of matrices;
- skills in solving systems of ordinary differential equations using matrix methods;
- skills in using a linear algebra software package for operations on matrices. and for implementing matrix numerical techniques.
Appreciate:
- the power and importance of abstract linear algebra techniques in solving concrete problems in numerical analysis, science, the social sciences and engineering.
Content:
Vector Spaces: vector spaces; norms; inner products; linear transformations; application to Fourier series. Matrices: review of general properties of matrices - multiplication, inverse, transpose, partitioning; computing determinants, inverses, rank; LU - factorisation. Eigenvalues: Eigenvalues of square matrices; multiplicity of eigenvalues; eigenvalues and eigenvectors of special matrices, including triangular, hermitian, real symmetric and positive definite matrices; diagonalisation of matrices by unitary matrices and by nonsingular matrices; Jordan canonical form; minimal polynomial; Cayley - Hamilton theorem; spectral decomposition; diagonalisation of quadratic forms; positive definite forms. Differential Equations: systems of ordinary differential equations; Laplace transforms; control systems; stability; Gershgorin's circle theorem; estimation of dominant eigenvalue. Coding theory: linear codes; generator and parity check matrices; Hamming distance, encoding and decoding; error-detecting and error-correcting codes; syndromes and standard arrays; hamming codes and perfect codes.
Assessment:
Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.
1. Mathematics, Faculty of Science (v4, p210) : Next:618-222 | Prev:618-211
2. Math. & Stats., Faculty of Educ(Parkville) (v5, p146) : Next:618-231 | Prev:618-200
Credit points: 12.0
Coordinator: Dr J J Koliha.
Prerequisite: One of Mathematics 618-102 (1995 Handbook) 618-112, 618-122, 618-200, 618-211.
Contact: 39 lectures (three each week)
Timetable: Second semester.
Objectives:
On completion of this subject, students should:Comprehend:
- basic and more advanced concepts of linear algebra such as vector spaces, inner product spaces, linear transformations, diagonalization of matrices, Jordan canonical form and spectral decomposition.
Have developed:
- skills in calculating eigenvalues and eigenvectors including iterative methods;
- skills in the diagonalization of matrices;
- skills in solving systems of ordinary differential equations using matrix methods;
- skills in using a linear algebra software package for operations on matrices. and for implementing matrix numerical techniques.
Appreciate:
- the power and importance of abstract linear algebra techniques in solving concrete problems in numerical analysis, science, the social sciences and engineering.
Content:
Vector Spaces Vector spaces; norms; inner products; linear transformations; application to Fourier series. Matrices Review of general properties of matrices - multiplication, inverse, transpose, partitioning; computing determinants, inverses, rank; LU - factorisation. Eigenvalues Eigenvalues of square matrices; multiplicity of eigenvalues; eigenvalues and eigenvectors of special matrices, including triangular, hermitian, real symmetric and positive definite matrices; diagonalisation of matrices by unitary matrices and by nonsingular matrices; Jordan canonical form; minimal polynomial; Cayley - Hamilton theorem; spectral decomposition; diagonalisation of quadratic forms; positive definite forms. Differential Equations Systems of ordinary differential equations; Laplace transforms; control systems; stability; Gershgorin's circle theorem; estimation of dominant eigenvalue. Coding theory Linear codes; generator and parity check matrices; Hamming distance, encoding and decoding; error-detecting and error-correcting codes; syndromes and standard arrays; hamming codes and perfect codes.
Assessment:
Up to 26 pages of written assignments and up to three hours of end-of-semester written examination.
* Note that CONTACT, CONTENT, PREREQUISITES differs from the maintainer's version above. A log of variations is available.
2. Math. & Stats., Faculty of Educ(Parkville) (v5, p146) : Next:618-231 | Prev:618-200
Status: Official 1996 Date created: Oct 9 1995 Last modified: Oct 9 1995 Authorised by: Academic Registrar Email enquiries: Course_Information@registrar.unimelb.edu.au
Maintained by: Dept. of Mathematics, Faculty of Science.
Copyright © University of Melbourne 1995,1996.