Linear Algebra (Theory)

Paper Code: 
24CBDA513
Credits: 
03
Periods/week: 
03
Max. Marks: 
100.00
Objective: 

This course will enable students to 

1. Understand the basic concepts of linear algebra.

2. Understand the applications of linear algebra with respect to Data Science and Artificial Intelligence

 

Course Outcomes: 

Course

Learning outcome

(at course level)

Learning and teaching strategies

Assessment Strategies

Course Code

Course

Title

24CBDA513

Linear Algebra

(Theory)

 

CO283. Apply properties of matrices- and matrix algebra to solve real-world problems.

CO284. Appraise the concepts of vector space, linear dependence and independence in solving data based problems.

CO285. Apply linear transformations, and their corresponding matrices.

CO286. Design and solve problems in linear and inner product spaces for data science applications.

CO287. Build a solution for real-world problems using Linear Algebra concepts with machine learning algorithms.

CO288.Contribute effectively in course-specific interaction

Approach in teaching: Interactive Lectures, Discussion, Reading assignments, Demonstration.

 

Learning activities for the students: Self learning assignments, Effective questions, Seminar presentation.

 

Class test, Semester end examinations, Quiz, Assignments, Presentation.

 

9.00
Unit I: 
Matrices and System of linear equations

Matrix, Operation on matrices, Transposes and Powers of Matrices, Zero, One Matrices, Diagonal Matrix, Inverse of Matrix, System of Linear equations and Matrices, System of Homogeneous and non-homogeneous equations, Cayley Hamilton Theorem, Eigenvalues, Eigenvectors and diagonalization.

 

9.00
Unit II: 
Vector Spaces

Vector space-Examples and Properties- Subspaces-criterion for a subset to be a subspace- linear span of a set- linear combination- linear independent and dependent subsets- Basis and dimensions- Standard properties- Examples illustrating concepts and results.

 

9.00
Unit III: 
Linear Transformations

Linear transformations, properties, matrix of a linear transformation, change of basis, range and kernel, rank and nullity, Rank-Nullity theorem.

 

9.00
Unit IV: 
Norms and Inner Product Spaces

Introduction, Inequalities on Linear Spaces, Norms on Linear Spaces, Inner products Orthogonally, Unitary and Orthogonal Matrices, norms for matrices.

 

9.00
Unit V: 
Linear Algebra Applications in Data Science

Linear Algebra in Machine Learning, Loss functions, Regularization, covariance Matrix, Support Vector Machine Classification. Linear Algebra in dimensionality Reduction, Principal Component Analysis (PCA), Singular Value Decomposition (SVD).

 

ESSENTIAL READINGS: 

Suggested Text Books

  1. David C. Lay- Linear Algebra and its Applications- 5th ed.-Indian Reprint- Pearson Education Asia- 2018.
  2. M.P. Deisenroth, A. Aldo Faisal and C.H. Ong- Mathematics for Machine Learning 1st ed.
    1. Cambridge University Press, 2020.
  3. V. Krishnamurthy- V. P. Mainra- and J. L. Arora- An introduction to linear algebra. New Delhi India. Affiliated East East-West Press Pvt Ltd.- 2003.

 

REFERENCES: 

SUGGESTED REFERENCE BOOKS

  1. K.P.  Murthy, Machine Learning- a Probabilistic Perspective, MIT Press, 2012.
  2. S. H. Friedberg- A. Insel- and L. Spence- Linear algebra- 4th ed.- Pearson- 2015.
  3. Gilbert Strang- Linear Algebra and its Applications- 4th ed.- Thomson Brooks/Cole- 2007.

e RESOURCE

  1. NOC,Advance Linear Algebra,IIT Rookee :https.//nptel.ac.in/courses/106106222

 

 JOURNALS

  1. Journal of the Brazilian Computer Society, SpringerOpen, https://journal-bcs.springeropen.com/
  2. Journal of Internet Services and Applications, SpringerOpen: https://jisajournal.springeropen.com/

 

Academic Year: 
2024-25
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