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Course Detail


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)


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

CO1 3 2 1
CO2 3 3 2
CO3 3 3 2
CO4 3 2 1

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