Monash University Handbook

Vector spaces, linear transformations. Determinants, eigenvalue problems. Inner products, symmetric matrices, quadratic forms. Linear functionals and dual spaces. Matrix decompositions, least squares approximation, power method. Applications to areas such as coding, economics, networks, graph theory, geometry, dynamical systems, Markov chains, differential equations.

Outcomes

On completion of this unit students will be able to:

Understand concepts related to vector spaces, including subspace, span, linear independence and basis;
Understand properties of linear transformations and identify their kernel and range;
Diagonalize real matrices by computing their eigenvalues and finding their eigenspaces;
Understand matrix decomposition techniques;
Understand concepts related to inner product spaces and apply these to problems such as least-squares data fitting;
Develop and apply tools from linear algebra to a wide variety of relevant situations;
Understand and apply relevant numerical methods and demonstrate computational skills in linear algebra;
Present clear mathematical arguments in both written and oral forms;
Develop and present rigorous mathematical proofs.

Assessment

End of semester examination (3 hours): 60% (Hurdle)

Continuous assessment: 40% (Hurdle)

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for both the end-of-semester examination and continuous assessment components.