LINEAR ALGEBRA

Paper Code: 
MAT221
Credits: 
5
Contact Hours: 
75.00
Max. Marks: 
100.00
Objective: 

This course will enable the students to –

 

  1. Understand the history of mathematics and its recent areas. 
  2. Understand the diverse role of mathematics in social and economic areas through independent learning.
  3. Identify, understand and discuss current, real-world issues.
  4. Improve oral and written communication skills.
  5. Apply principles of ethics and respect in interaction with others.

Course Outcomes (COs):

Learning outcomes (at course level

Learning and teaching strategies

Assessment Strategies

 

The students will be able to –

 

CO26: Use multiple thinking strategies to examine real-world issues, explore creative avenues of expression, solve problems, and make consequential decisions.

CO27: Acquire, articulate, create and convey intended meaning using verbal and non-verbal method of communication that demonstrates respect and understanding in a complex society.

CO28: Apply principles of ethical leadership, collaborative engagement, socially responsible behavior, respect for diversity in an interdependent world, and a service-oriented commitment to advance and sustain local and global communities.

Approach in teaching:

Group Discussion,

Classroom Problem Solving Sessions

 

Learning activities for the students:

Field activities

Seminar

Presentation

Subject based  Activities

Class test, Semester end examinations, Quiz, Solving problems in tutorials, Assignments, Presentation, Individual and group projects

 

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, Similarmatrices, 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 ofbilinear 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 & Ray Kunze, Linear Algebra, Prentice-Hall of India Pvt. Ltd., 1971.
  • K.B.Datta, Matrix and Linear Algebra, Prentice-Hall of IndiaPvt., Limited, Feb 1, 2004.
  • A.Ramachandra Rao and Bhimasankaram, Linear Algebra, Second Edition, Hindustan Book Agency, 2017.
References: 
  • 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 PublishingHouse, 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: 
2019-2020
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