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 ApplicationsJames 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 
midexam  30 
endexam  50 
Last Update: 03/02/2024

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