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

Paper Code

Paper Title

MAT221

 

 

 

 

 

 

 

Linear Algebra

(Theory)

 

 

 

 

 

 

 

The students will be able to:

 

CO29: Identify and construct linear transformations of a matrix.
CO30: Characterize linear transformations as onto, one-to-one.
CO31: Solve linear systems represented as linear transforms.
CO32: Express linear transforms in other forms, such as matrix equations and vector equations.

CO33: Characterize a set of vectors and linear systems using the concept of linear independence.

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, eigen values, 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 eigen values, 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: 
  • Kenneth Hoffman and Ray Kunze, Linear Algebra, Prentice-Hall of India Pvt. Ltd., 1971.
  • 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, 1994.
  • Ben Noble, James W. Daniel, Applied Linear Algebra, Prentice-Hall of India, 1987.
  • I.N. Herstein, Topics in Algebra, Wiley Eastern Ltd., New Delhi, 1975.
  • I.S. Luther and I.B.S. Passi, Algebra, Vol. I Groups, Narosa Publishing House, Vol. I, 1996.
  • Seymour Lipschutz, Linear Algebra, McGraw Hill, 2001.
  • Kenneth Hoffman and Ray Kunze, Linear Algebra, Prentice –Hall of India, Pvt. Ltd., 1971.

 

Academic Year: 
2020-2021
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