Linear Algebra

Paper Code: 
MAT 221
Credits: 
5
Contact Hours: 
75.00
Max. Marks: 
100.00
Objective: 

This course will enable the students to –

  1. Understand the concept of systems of linear equations, linear span, linear independence, basis and dimension.
  2. Understand how to apply these concepts in various vector spaces and subspaces. 
  3. Understand Compute and use eigenvectors and eigen values.

 

Course Outcomes (COs):

Course

Learning outcomes

(at course level)

Learning and teaching strategies

Assessment

Strategies

Course Code

Course Title

MAT221

 

 

 

 

 

 

 

 

Linear Algebra

(Theory)

 

 

 

 

 

 

 

The students will be able to:

 

CO36: Describe vector spaces and their applications in real life problems.
CO37: Differentiate between linear transformations and functions defined on the same domain.
CO38: Identify eigenvalues, eigenvector of various metrices
CO39: Describe bilinear forms, quadratic forms, related properties, theorems and their uses.

CO40: Use the knowledge of inner product spaces in security systems.

CO41: Analyse orthogonality, various inequalities and their applications in real life problems.

 

Approach in teaching:

Interactive Lectures, Discussion, Tutorials, Demonstrations, Team teaching, Teaching using advanced IT audio-video tools

 

Learning activities for the students:

Self-learning assignments, Effective questions, Simulation, Seminar presentation, Giving tasks

Assessment Strategies

Class test, Semester end examinations, Quiz, Solving problems in tutorials, Assignments, Presentation.

 

 

Unit I: 
I
15.00

Linear transformation of vector spaces, Dual spaces, Dual basis and their properties, Dual maps, Annihilator. 

Unit II: 
II
15.00

Matrices of a linear map, Matrices of composition maps, Matrices of dual map, eigenvalues, eigen vectors, Rank and nullity of linear maps and matrices, Invertible matrices, Similar matrices, Diagonalization of matrices.

Unit III: 
III
15.00

Determinants of matrices and its computations, Characteristic polynomial and eigenvalues, Minimal polynomial, Cayley-Hamiltton theorem.

Unit IV: 
IV
15.00

Bilinear forms: Definition and examples, Matrix of a bilinear form, Orthogonality, Classification of bilinear forms, Quadratic forms.

Unit V: 
V
15.00

Real inner product space, Schwartz’s inequality, Orthogonality, Bessel’s inequality, Adjoint, Self-adjoint linear transformations and matrices, orthogonal linear transformation and matrices, Principal axis theorem.

Essential Readings: 
  • Dileep S. Chauhan and K.N. Singh, Studies in Algebra, JPH, Jaipur, 2011.
  • Kenneth Hoffman and Ray Kunze, Linear Algebra, Pearson 2018.
  • K.B. Datta, Matrix and Linear Algebra, Prentice-Hall of India Pvt., Limited, 2004.
  • Ramachandra Rao and Bhimasankaram, Linear Algebra, Second Edition, Hindustan  Book Agency, 2017.
  • M. Artin, Algebra, Prentice-Hall of India, 2007.
References: 
  • Ben Noble, James W. Daniel, Applied Linear Algebra, Prentice-Hall of India, 1987.
  • I.N. Herstein, Topics in Algebra, Wiley Eastern Ltd., New Delhi, 2006.
  • I.S. Luther and I.B.S. Passi, Algebra, Vol. I Groups, Narosa Publishing House, Vol. I, 1997.
  • Seymour Lipschutz, Linear Algebra, McGraw Hill, 2018.
Academic Year: 
2023-2024
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