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Amrik Sen, PhD (Applied Mathematics, University of Colorado, Boulder, USA)
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 -- spring-mass dynamical system
Lecture-1: 16/01/25
Set 2: Motivation -- spring-mass dynamical system
Lecture-2: 21/01/25
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notes here
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code (numerical solver) here
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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
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notes here
errata: last pg., set u2 = α; then u1 = α+1.
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recording here
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
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notes here (part-1 of the discussion can be found in Set 9)
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recording here
Set 11: Linear transformation | Inverse of a matrix (GJ method)
Lecture-11: 27/02/25
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notes here (Linear maps)
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notes here (Matrix inverse using Gauss-Jordan method)
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recording here
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
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notes here
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}.
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recording here
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
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notes: simple LS regression here
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notes: multi-dimensional LS regression here
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What is the meaning of a derivative of a scalar valued function with respect to a vector? here
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code-1 here, code-2 here
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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)
Computational assessment-L2: here (Cryptography)
Phenomenology assessment L2: (The Circle of Life)
Phenomenology assessment L1: (The Alchemist and Mathemagic)
Q10: either response marked in red will be considered correct.
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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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