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Basic Details:

  • Course Code: EM 1020
  • Credits: 3
  • Pre-requisites: None
  • Compulsory/Optional: Compulsory

Aim :

To encourage students to develop a working knowledge of the central ideas of linear algebra: vector spaces, linear transformations, orthogonality, eigenvalues, eigenvectors and canonical forms and the applications of these ideas in science and engineering.

Intended Learning Outcomes:

On successful completion of the course, the students should be able to;

  • Apply the knowledge of matrices, Gaussian reduction and determinants to solve systems of linear equations.
  • Apply the properties of vector spaces and to generalize the concepts of Euclidean geometry to arbitrary vector spaces.
  • Identify linear transformations, represent them in terms of matrices, and interpret their geometric aspects.
  • Calculate eigenvalues and eigenvectors of matrices and linear transformations and apply the concepts in physical situations.
  • Prove eigenvalue properties of real symmetric matrices and apply them in quadratic forms.

Couse Content:

Operations, elementary matrices, inverse, partitioned matrices.

Introduction and properties.

Definition, subspaces, linear independence and spanning, basis, change of basis, normed spaces, inner product spaces, Gram-Schmidt orthonormalization.

Introduction, matrix representation, operations of linear transformations, change of basis.

Gauss and Jordan elimination; LU factorization, least square approximations, ill-conditioned and over-determined systems.

Computing eigenvalues and eigenvectors, Eigen-basis, diagonalization, matrix exponentials.

Properties, definiteness, quadratic forms, applications.

Time Allocation (Hours):

Lectures
0
Assignments
0

Recommended Texts:

  • Gilbert Strang, “Introduction to Linear Algebra”, 5th edition (2010), Cambridge Press.
  • David C. Lay, S.R.Lay & J.Mcdonald, “Linear Algebra and its Applications”, 5th edition (2012), Pearson.
  • David Poole, “Linear Algebra: A Modern Introduction”, 4th edition (2005), Cengage.
  • Thomas S. Shores, “Applied Linear Algebra and Matrix Analysis”, 2007, Springer.

Assessment:

In - course:

Tutorials/Assignments
20%
Mid Semester Examination
30%

End-semester:

50%