Linear Algebra

Paper Code: 
CBDA 513
Credits: 
3
Periods/week: 
3
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. (COs).

Course Outcome (at course level)

Learning and teaching strategies

Assessment Strategies

On completion of this course, the students will:

CO236. Use properties of matrices- especially inevitability and matrix algebra.

CO237. Describe the concepts of vector space, linear dependence and independence.

CO238. Apply linear transformations and their corresponding matrices and understand the Rank and nullity concepts.

CO239. Apply the concepts of linear space and inner product space in Data Science.

CO240. Apply the concepts of Linear Algebra in machine learning algorithms.

 

Interactive Lectures, Discussion, Reading assignments, Demonstration.

Class test, Semester end examinations, Quiz, Assignments, Presentation, Individual and group projects, Peer Review.

 

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.

 

Unit 5 Linear Algebra Applications in Data Science                                                                                 9 hrs

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).

 

 

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.
    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: 
  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

 

 JOURNALS

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

 

 

 

Academic Year: 
2023-24
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