GP116 Linera Algebra

Course Code
GP116
Course Title
Linera Algebra
Credits
3
Course Type
CORE
Aims/Objectives
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 (ILOs)
Knowledge:
At the end of this course, a student will 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
Skill:
At the end of this course, a student will be able to;
  • 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
Textbooks and References
  • Advanced Engineering Mathematics - E. Kreyszig
  • Elementary Linear Algebra and its Applications-James W. Daniel
  • Matrices for Scientists and Engineers - W.W. Bell
  • Linear Algebra with Applications - H.G. Campbell
  • Elementary Linear and Matrix Algebra. The view point of Geometry- John T. Moore
  • Matrix Algebra for Engineers - J.M. Gere
  • Introduction to Linear Algebra- Gilbert Strang
Topic Time Allocated / hours
L T P A
Matrix Algebra
Matrix Operations; Types of matrices; Elementary row column operations; Rank and Inverse; Partitioned matrices; Matrix Factorization 		- - - -
Determinants
Introduction; Properties 		- - - -
Systems of linear Equations
Matrix representation; Existence and uniqueness of a solution; Solving techniques 		- - - -
Vector Spaces
Definition and examples; Subspaces; Linear independence, Spanning, Basis and dimension; Coordinates and change of basis; Normed spaces and Inner product spaces; Least squares problem 		- - - -
Solving the Least squares problem/Linear Transformations
- 		- - - -
Linear Transformations
What is a linear transformation; Subspaces associated with a linear transformation; How do you represent a linear transformation as a matrix with respect to a given basis 		- - - -
Eigenvalues and eigenvectors
What are Eigenvalues and Eigenvectors and their physical significance; Given a matrix how do you find the Eigenvalues and the associated Eigenvectors; Characteristic equation and the Cayley Hamilton theorem; Applications of Cayley Hamilton theorem; Algebraic and the geometric multiplicity of an Eigenvalue and the existence of an Eigenbasis; Diagonalization of a matrix; Computing matrix exponential; What is a deficient matrix; How do you find generalized eigenvectors; Jordan form for a deficient matrix; Symmetric matrices and orthogonal diagonalization 		- - - -
Quadratic Forms
Use the quadratic forms to analyse geometrical objects such as central conics; Use features of quadratic forms to analyse mechanical systems modelled as differential equations 		- - - -
Total (hours)
36 - - 18

L = Lectures, T = Tutorial classes, P = Practical classes, A = Homework Assignments

Assessment Percentage Marks
assignments 20
mid-exam 30
end-exam 50
Last Update: 03/02/2024 | Edit this page