 COURSE SUMMARY
Course Title:
Linear Algebra
Course Code:
19MAT112
Year Taught:
2019
Semester:
2
Degree:
School:
School of Engineering
Campus:
Bengaluru
Chennai
Coimbatore
Amritapuri

'Linear Algebra' is a course offered in the second semester of  B. Tech. programs at the School of Engineering, Amrita Vishwa Vidyapeetham.

### 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

#### 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 / REFERENCES

Text Book:

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.