Linear Algebra

Paper Code: 
25CBDA513
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

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25CBDA513

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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

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: 

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.

   a.   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 READINGS:

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: 
2025-26
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