20 credits at level HE5
• To develop systematic techniques for solving systems of linear equations
• To introduce the concepts of vector space, subspace and linear transformation, by building upon study of groups from Level 1
• To introduce the notions of basis, eigenvalue and eigenvector, and their relationship to diagonalising a matrix representing a linear transformation
• To introduce inner product spaces.
Linear equations and matrices.
Vectors and their operations.
Vector space theory.
Basis and dimension.
Kernel and image spaces.
Eigenvalues, eigenvectors and the diagonalisation of matrices.
Inner products and inner product spaces.
Approximately half the available class contact time will be devoted to lectures based on the use of printed notes and the remainder to group or individual problem solving. Students will be expected to do a significant amount of private study to keep in step with the lectures and problem solving sessions.
Two pieces of coursework will be set, each to be completed by a prescribed date in the students’ own time. There will be a formal closed-book examination of 2¼ hours duration at the end of the module.
when you have successfully completed this module you will:
to demonstrate that you have achieved the learning outcome you will:
|1.||have fluency with the use of row operations.||apply row operations to solve systems of linear equations and to find the inverse of a matrix.|
|2.||have an understanding of the concepts of vector space, subspaces and linear transformations.||show that the vector space axioms are satisfied for an algebraic structure, demonstrate that a subset forms a subspace, and verify that a mapping is a linear transformation.|
|3.||have an understanding of the concept of a basis of a vector space.||show that a set of vectors is linearly independent and spans a vector space.|
|4.||have an understanding of eigenvalue and eigenvectors.||find the eigenvalues and the eigenvectors of a matrix.|
|5.||have an understanding of inner products and symmetric linear tranformations.||show that a mapping is an inner product, and represent a symmetric linear transformation by a diagonal matrix relative to an orthonormal basis of eigenvectors.|
Your achievement of the learning outcomes for this module will be tested as follows:
|Description||Two pieces of coursework to be complted outside class time.||Unseen written examination.|
Before taking this module you must have successfully completed the following:
No restrictions apply.
Anton, H. and Busby, R.C. Contemporary Linear Algebra, Wiley (2003).
Blyth, T.S. and Robertson, E.F. Basic Linear Algebra, Springer (2002).
Broida, J.G. and Williamson, S.G. A Comprehensive Introduction to Linear Algebra, Addison-Wesley (1989).
Friedberg, S.H., Insel, A.J. and Spence, L.E. Linear Algebra,
Griffel, D.H. Linear Algebra and its Applications, Ellis Horwood Ltd. (1989).
Johnson, L.W., Riess, R.D. and Arnold, J.T. Linear Algebra
Kaye, R. and Wilson, R Linear Algebra, OUP (1998).
Kolman, B. Introductory Linear Algebra, Prentice-Hall (1997).
Lipshutz, S Schaum's Outline of Theory and Problems of Linear Algebra, 2nd. ed., McGraw Hill , (1991).
Penney, R.C. Linear Algebra: Ideas and Applications, Wiley (1998).
Strang, G Linear Algebra and its Applications, 3rd edition
Harcourt Brace (1988).
Towers, D. Guide to Linear Algebra, Macmillan (1988).
Wright, D.J. Introduction to Linear Algebra, McGraw-Hill (1999).
|Host Subject Group:||Mathematics|
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