MLS01 LINEAR ALGEBRA AND ITS APPLICATIONS
SPEAKERS - DEVANG BAJPAI, PURNIMA TIWARI, ARPIT TRIVEDI, AAYUSH
VERMA, KRISHNAKANT YADAV
Dates - 21 Oct 2024 - 15 Nov 2024
Venue - Mathematics Lab, SBS
Theoretical Nexus
Webpage - https://sites.google.com/view/theoreticalnexus/lecture-
series/mls/mls01-linear-algebra-and-its-application
This will be an inaugural fall tutorial lecture series for the Madhava
Lecture Series (MLS). The motivation behind this lecture series is to dis-
cuss and communicate on different topics in Linear Algebra. Our plan is
to discuss topics which include (but, as always, not limited to) Set The-
ory, Fields, Vector Spaces, Eigenvalues and Diagonalization, Normed Vector
Spaces, Dirac Bra-ket, Application to Quantum Mechanics of Linear Al-
gebra, Hilbert Spaces, Modules over Ring. The intention is to create a
bottom-to-top approach to discussing the above mentioned matters.
Course Description
Linear algebra is the mathematics that is ubiquitous in many fields of
mathematics, physics, and computer science, to name a few. It is a rich
subject with very old insights and ideas about matrices, system of equations,
polynomials, abstract stuff like vector spaces, and norms. Our goal is to
enhance the understanding among these few chosen lines since covering the
entire linear algebra is ambitious at this point in short period. However,
we wish to advance in the right direction as well as discussing some of the
application which are immediate the subject of quantum mechanics.
Linear algebra deals with majorly three important points.
(1) It deals with the study of vector spaces over a field.
(2) It deals with the transformation and mappings of these vector spaces.
Email address:
bajpaidevang25@gmail.com,
purnima162.21@gmail.com,
aayushverma6380@gmail.com
Note to attendants: You are suggested to keep checking the webpage for updated
syllabus and schedule. No registration is required, you can just join us at the given venue.
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SPEAKERS - DEVANG BAJPAI, PURNIMA TIWARI, ARPIT TRIVEDI, AAYUSH VERMA, KRISHNAKANT YADAV
(3) It deals with solving a system of equations and their linear transfor-
mations.
Historically, solving a matrix can be traced back to Babylons (linear
equations with two unknowns) and also Bhaskara II. It was Leibniz who
connected these systems with determinants and then Cramer. In 1848, J.J.
Sylvester introduced the term “matrix”. Arthur Cayley worked on the ma-
trix algebra (its multiplication and addition).
Until the end of 19th century, linear algebra was heavily being used in
physics and became an integral part of quantum mechanics. In quantum
mechanics, we say the operators are basically matrices acting on the states
(wavefunctions) and yielding an eigenvalue.
Vector spaces are basically just modules over a ring R with R also being
a field.
There are many intricate facets of Linear Algebra, especially its rich alge-
bra structure. We hope to cover these special features in our series MLS01.
Tentative Schedule
For the up-to-date schedule, please keep checking the series webpage. We
will send more suggested readings (decided by individual speakers) with our
each email announcement.
• Lecture 1: The Story from Set and Basics of Linear Algebra
by Arpit Trivedi (21 Oct 2024, Mon)
• Lecture 2: Introduction to Vectors, different Spaces and Sub-
spaces by Arpit Trivedi (23 Oct 2024, Wed)
• Lecture 3: TBA by Purnima Tiwari (28 Oct 2024, Mon)
• Lecture 4: TBA by Krishnakant (06 Nov 2024, Wed)
• Lecture 5: TBA by Devang Bajpai (08 Nov, 2024, Fri)
• Lecture 6: TBA by Devang Bajpai (13 Nov, 2024, Wed)
• Lecture 7: TBA by Purnima Tiwari (15 Nov, 2024, Fri)
• Lecture 8: Modules over Ring, Affine Geometry and Opera-
tor Algebra by Aayush Verma (18 Nov, 2024, Mon)
• Discussion Session
Suggested Readings and References
• Linear Algebra Done Right by Sheldon Axler
• Linear Algebra by Serge Lang
• Finite-dimensional vector spaces by Paul Halmos
• Abstract Algebra by Dummit and Foote
• Naive Set Theory by Paul Halmos
• Linear Geometry by Gruenberg
• Introduction to Quantum Mechanics by D Griffiths
• Zweibach lectures on Quantum Mechanics 8.05, https://ocw.mit.edu/courses/8-
05-quantum-physics-ii-fall-2013/resources/lecture-5-linear-algebra-vector-
spaces-and-operators/
