Linear Algebra

Paper Code: 
24DMAT811
Credits: 
6
Contact Hours: 
90.00
Max. Marks: 
100.00
Objective: 

This course will enable the students to –

  1. Apply the concept of systems of linear equations, linear span, linear independence, basis and dimension.
  2. Develop and apply these concepts in various vector spaces and subspaces.
  3. Compute and use eigenvectors and eigenvalues.

 

Course Outcomes: 

 Course

Learning outcomes

(at course level)

Learning and teaching strategies

Assessment

Strategies

Course Code

Course Title

 

 

 

 

 

 

 

24DMAT

811

 

 

 

 

 

 

Linear Algebra

(Theory)

CO180: Differentiate between linear transformations and functions defined on the same domain.

CO181: Create eigenvalues, eigenvectors of various metrics.

CO182:  Compute polynomials using determinants.

CO183: Describe bilinear forms, quadratic forms, related properties, theorems and their uses.

CO184: Apply the knowledge of inner product spaces in security systems.

CO185: Contribute effectively in course-specific interaction.

Approach in teaching:

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

 

Learning activities for the students:

Self-learning assignments, Effective questions,  Assigned tasks

 

 

Class test, Semester end examinations, Quiz, Solving problems in tutorials,

 

 

Unit I: 
Linear Transformation
18.00

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

 

Unit II: 
Matrices
18.00

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: 
Determinants
18.00

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

 

Unit IV: 
Bilinear forms
18.00

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

 

Unit V: 
Inner Product Space
18.00

Real inner product space, Schwartz’s inequality, Orthogonally, 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.

 e- RESOURCES

●    https://nptel.ac.in/courses/111106051

●    https://nptel.ac.in/courses/111104137

●    https://nptel.ac.in/courses/111106135

●    https://www.digimat.in/nptel/courses/video/111101115/L01.htm

 JOURNALS

●    https://www.journals.elsevier.com/journal-of-algebra

●    https://www.worldscientific.com/worldscinet/jaa

●    https://www.springer.com/journal/10469

 

Academic Year: 
2024-2025
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