Back close
Admissions

Course Detail

Course Name Linear Algebra
Course Code 26DLS501
Program M. Sc. in Data Science with Logistics and Supply Chain Management
Semester 1
Credits 4
Campus Coimbatore

Syllabus

Unit 1

General   Vector Spaces: Real Vector Spaces – Sub Spaces – Linear Independence – Coordinates and Basis – Dimension-Change of Basis. (10 Hrs)

Unit 2

Inner Product Spaces: Inner Products – Angles, Length and Distance-Orthogonality- Orthogonal Complements – Orthogonal Projections -Orthogonal Basis- Gram Schmidt Process-Least Square Principle. (Case Study) (15 Hrs)

Unit 3

Unit III Linear Transformations: General Linear Transformation – Kernel and Range of a Linear Transformation – Compositions and Inverse of Linear Transformation – Matrices of Linear Transformations – Positive Definite Matrices – Symmetric and Skew Symmetric Matrices-Matrix Norm. (15 Hrs)

Unit 4

Eigen values and Eigen vectors: Problems in Eigen Values and Eigen Vectors, Orthogonal Diagonalization, Quadratic Forms, Diagonalizing Quadratic Forms. (10 Hrs)

Unit 5

LU, QR and Singular Value decompositions. (10 Hrs)

Text Books / References

Text Books

  1. Howard Anton and Chris Rorres, “Elementary Linear Algebra with Supplemental Applications”, 11th Edition, John Wiley & Sons, Inc., 2016.
  2. Gilbert Strang, “Introduction to Linear Algebra”, 5th Edition, Wellesley-Cambridge Press, 2016.

 References

  1. Kenneth Hoffmann and Ray Kunze, “Linear Algebra” Second Edition, Prentice Hall, 1971.
  2. Mike Cohen, Practical Linear Algebra for Data Science, O’Reilly Media, Inc., Publisher, 2022 

 

 

Objectives and Outcomes

Course Outcomes
CO1 To understand the axioms in the definition of a vector space, subspaces, basis, dimension; To learn to change the basis.
CO2 To understand and compute inner products, the length of a vector, angle and distance between vectors, orthogonal complement, projection and orthonormal basis from any arbitrary basis. To learn the least square principle.
CO3 To understand the concepts of linear transformations and matrices for linear transformations.
CO4 To understand the concepts of eigen values, eigen vectors and diagonalization.
CO5 To learn to decompose matrices using various techniques.

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.

Admissions Apply Now