Course Detail

 Course Name Linear Algebra Course Code 19MAT112 Program B. Tech. in Electrical and Electronics Engineering, B. Tech. in Civil Engineering, B. Tech. in Aerospace Engineering, B. Tech. in Computer and Communication Engineering Semester Two and Five Year Taught 2019

Syllabus

Review of matrices and linear systems of equations. (2 hrs)

Vector Spaces : Vector spaces – Sub spaces – Linear independence – Basis – Dimension – Inner products – Orthogonality – Orthogonal basis – Gram Schmidt Process – Change of basis. (12 hrs)

Orthogonal complements – Projection on subspace – Least Square Principle. (6 hrs)

Linear Transformations : Positive definite matrices – Matrix norm and condition number – QR- Decomposition – Linear transformation – Relation between matrices and linear transformations – Kernel and range of a linear transformation. (10 hrs)

Change of basis – Nilpotent transformations – Similarity of linear transformations – Diagonalisation and its applications –

Jordan form and rational canonical form. (10 hrs)

SVD

Evaluation Pattern

Test-1 -15 marks (one hour test) after 15th lecture.

CA – 20 marks (Quizzes / assignments / lab practice) Test – 2- 15 marks (two-hour test) at the end of 30th lecture.

End semester- 50 marks (three hour test) at the end of the course. Total – 100 marks.

Supplementary exam for this course will be conducted as a three-hour test for 50 marks.

Text Books

1. Howard Anton and Chris Rorrs, “Elementary Linear Algebra”, Ninth Edition, John Wiley & Sons, 2000. Reference Book:
2. Poole, Linear Algebra: A Modern Introduction, 2nd Edition, Brooks/Cole, 2005.
3. Gilbert Strang, “Linear Algebraand its Applications”, Third Edition, Harcourt College Publishers, 1988.

Objectives and Outcomes

Course Outcomes

 CO1 Understand the basic concepts of vector space, subspace, basis and dimension CO2 Understand the basic concepts of inner product space, norm, angle, Orthogonality and projection and implementing the Gram-Schmidt process, to obtain least square solution CO3 Understand the concept of linear transformations, the relation between matrices and linear transformations, kernel, range and apply it to change the basis, to get the QR decomposition, and to transform the given matrix to diagonal/Jordan canonical form. CO4 Understand the concept of positive definiteness, matrix norm and condition number for a given square matrix.

CO-PO Mapping

 PO1 PO2 PO3 PO4 CO1 3 2 1 CO2 3 3 2 CO3 3 3 2 CO4 3 2 1

DISCLAIMER: The appearance of external links on this web site does not constitute endorsement by the School of Biotechnology/Amrita Vishwa Vidyapeetham or the information, products or services contained therein. For other than authorized activities, the Amrita Vishwa Vidyapeetham does not exercise any editorial control over the information you may find at these locations. These links are provided consistent with the stated purpose of this web site.