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Computational Linear Algebra
(course code: FM 126)

Course instructor:

Amrik Sen

Course TAs:
Rajat Singla

Vijay Sahani
Sakshi Jaiswal

Emails:
amrik.sen@plaksha.edu.in
rajat.singla@plaksha.edu.in

vijay.sahani@plaksha.edu.in
sakshi.jaiswal@plaksha.edu.in

Office hours:
Amrik Sen (W - 14:40 to 15:30 hrs at A2-103)

Rajat Singla (MWF - 16:00 to 17:00 hrs at A2-WS-432)

Vijay Sahani (MWF - 16:00 to 17:00 hrs at A2-WS-433)  


Syllabus and manuals:                                                                                                 
Course Brochure (here)
Course etiquettes (here)


Python Tutorial (here)
Matlab tutorial (here)

 

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Lecture notes, python repository, and video recording links:                                                            
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Set 1: Motivation -- s
pring-mass dynamical system


Lecture-1: 16/01/25

Set 2: Motivation -- spring-mass dynamical system

Lecture-2: 21/01/25

  • notes here

  • code (numerical solver) here

  • recording here

Set 3: Vector spaces - definition, properties, examples                                                                                                                     
Lecture-3: 28
/01/25

Set 4: Linear independence | Span | Bases of vector spaces

 

Lecture-4: 30/01/25

 

Set 5: Row and column pictures of Ax = b                                                                                                                    
Lecture-5: 04/02/25

Set 6: Column space of a matrix | Geometrical interpretation                                                                                                          
Lecture-6: 06/02/25

      errata: last pg., set u2 = α; then u1 = α+1.

Set 7: RREF | Solving Ax = b using GJ method | Pivots, rank                                                                                           

Lecture-7: 11/02/25

 

 

Set 8: Null space of a matrix | Rank-nullity theorem                                                                                                                 
Lecture-8: 13/02/25

Set 9: Banking and accounting system as a vector space

Lecture-9: 18/02/25

Set 10: Col(A) Col(AA')

Lecture-10: 20/02/25

 

Set 11: Linear transformation | Inverse of a matrix (GJ method)

 

Lecture-11: 27/02/25

Set 12: Examples of linear transformation

Lecture-12: 04/03/25

Set 13: Change of bases matrices

Lecture-13: 06/03/25

 

 

Set 14: Abstraction | Introduction to eigenspace of a matrix

Lecture-14: 18/03/25

 

Set 15: Eigenvalues and eigenvectors

Lecture-15: 20/03/25

      errata-1: pg. 11 the reflection matrix pertains to reflection

      about the axis given by the line y=x and NOT the x-axis;

      errata-2: pg. 1 the eigenspace of a matrix is the set

      {EVs}{0}.

 

Set 16: Similarity transformation | Diagonalisable matrices

Lecture-16: 25/03/25

 

 

Set 17: Power method to find eigenvalues and eigenvectors

Lecture-17: 01/04/25

Set 18: Google page rank algorithm | Markov matrices

Lecture-18: 03/04/25

 

 

Set 19: Orthogonal projection | Orthonormal (ON) bases

Lecture-19: 08/04/25

 

Set 20: Gram-Schmidt procedure for ON bases

Lecture-20: 15/04/25

 

Set 21: QR factorization and Gram-Schmidt process

Lecture-21: 17/04/25

Set 22: Matrix model of least squares regression

Lecture-22: 22/04/25

  • notes: simple LS regression here

  • notes: multi-dimensional LS regression here

  • What is the meaning of a derivative of a scalar valued function with respect to a vector? here 

  • code-1 here, code-2 here 

  • recording here

 

 

Set 23: Application of QR factorization for least squares regression | Norms of vectors

Lecture-23: 24/04/25

Set 24: Jacobi and Gauss-Seidel iterative method

Lecture-24: 29/04/25

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MCQ Quiz-1

Section L1: here
Section L2: here

MCQ Quiz-2

Section L1: here

Section L2: here

Generative AI friendly assessment modules


Computational assessment-L1: here (Democratic communities)

  • Conceptual solution: here 

  • Python solution: here

Computational assessment-L2: here (Cryptography)

 

Phenomenology assessment L2: (The Circle of Life)

  • Multi-modal cue here

  • Response questionnaire here 

Phenomenology assessment L1: (The Alchemist and Mathemagic)

  • Multi-modal cue here

  • Response questionnaire here

Q10: either response marked in red will be considered correct. 

  • Python code of the Elixir model here

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Worksheets
 
Week 2: (20/1 - 24/1)
Basic matrix operations: here
Practice exercise: here

Laboratory workshop-1 notes: here
Laboratory worksheet-1: here
Laboratory worksheet-1 solutions: here


Week 3: (27/1 - 31/1)
Vector space: here

Laboratory workshop-2 notes: here
Laboratory worksheet-2: here
Laboratory worksheet-2 solutions: here

Week 4: (3/2 - 7/2)
Bases of vector spaces:
here

Laboratory workshop-3 notes: here
Laboratory worksheet-3: here

Laboratory worksheet-3 solutions: here

Week 5: (10/2 - 14/2)
Solved examples --> 

RREF | Rank of a matrix | Row transformations: here

Week 6: (17/2 - 21/2)
RREF | Bases of column & null spaces of a matrix: here


Week 7: (24/2 - 28/2)
Echelon form | Gauss-Jordan elimination: here

Week 11: (24/3 - 28/3)

Eigenvalues and Eigenvectors as a Linear Transformation:

here

Week 12: (31/3 - 04/04)

Power method to find evs and EVs: here

Week 14: (14/04 - 18/04)

Power method and orthogonal projections: here

Week 15: (21/04 - 24/04)

Gram-Schmidt and QR factorisation: here

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Sample practice problems for mid-sem exam
Problems: here

Mid-term examination paper - here

Sample practice problems for end-sem exam

Problems: here (topics post mid-sem)

End-semester exam paper - here


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+1-818-357-4698

skype id: amriksen

Los Angeles, CA, USA

© Amrik Sen 2017. 

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