The objective of this workshop is to make the students especially B.Tech students ready for the new generation jobs. Many universities are now offering courses with electives from various subject domains to mould their students to meet the requirements of the industry. So, to bring inter-disciplinary experimental active learning in our University, Center for Computational Engineering and Networking is organizing a 3-day course to reinforce linear algebra and optimization through experiments for modern signal processing and pattern classification.

Linear algebra, optimization (multivariate calculus + algorithms) and probabilistic graphical models have now become most essential subjects needed to tackle the problems in the era of automation and data science.

The common complaints to students regarding Linear algebra are

It is very abstract;

It contains too many new concepts; and

They don't know what uses it has.

One possible and viable solution at hand is

   Use Computational experiments to investigate and reinforce the concepts. Use Matlab as a Mathematical Laboratory. Example applications are plenty and are easy to demonstrate with in Matlab Environment. As the student progress from first year to fourth year, faculty may expose the students to newer and tougher problems and experiments. Most design and control problems in any Engineering are now tackled with above core subjects.

Years of acquaintance with students from various disciplines admitted to M.Techs, it is observed that , for many, Matrix is a a balck box. It simply is a rectangular array of numbers for them. They know the rules for finding certain quantities like determinant, eigenvalues and eigenvectors associated with a square matrix. Most of them could not tell a single application of these concepts.

So, finally for many, Advanced Mathematics means :

  A collection of rules if followed as per instruction proposed by teacher give solution to some well defined problems formulated by somebody (mainly the reference books authors).

This view need to be changed. The universe and its laws are described mainly by non-linear equations. Understanding nature of its behavior demands computational experiments.

Some of the concepts missed by B.Tech graduates in Linear Algebra are.

1. Matrix vector multiplication has two interpretations.
• Dot product interpretation
• Linear Combination interpretation
2. Matrix-Matrix multiplication has four interpretations / visualizations
• An ordered sequence of dot products
• Ordered Column wise linear combinations
• Ordered row wise linear combinations
• Sum of column-row outer products (sum of rank-1 matrices)

This in turn helps in understanding

3. The relationship between the ranks of A, B and AB.
4. Why column rank of a matrix is same as row rank of the matrix
5. Why A, A^TA and AA^T have same rank

This in turn helps in understanding

• Why A^TA and AA^T have same number of non-zero eigenvalues.
• The most famous Matrix decomposition called Singular-Value Decomposition

Understanding SVD properly helps in understanding

• How Google search engine works
• How simple Steganography and Watermarking works etc
6. The concept of Least-norm solution and Pseudo-Inverse
7. Concept of Orthogonality of functions and vectors and its use in Signal in Signal/ image processing and Communication Engineering. The lack of knowledge include principle behind the creation of
• Real discrete Fourier basis matrix
• Discrete Cosine Bases
• Walsh Hadamard bases
• Complex Fourier bases
• infinite such orthogonal bases using wavelet theory.
8. Digital Signal processing with the help of orthogonal matrices Filtering and removing specific components
9. Fundamental subspaces associated with a matrix and creation of their bases
10. Concept of Quadratic polynomials and characterization by signs of eigenvalues

In this workshop we aim

1. to discuss and offer computational experiments in matlab/python so as to get a firm grip on the tougher concepts in linear algebra.
2. to show how to use Linear algebra and basic optimization theory for signal processing and pattern classification.

1. Dynamic mode decomposition: An introduction - Prof. K. P. Soman
2. Fluid dynamics - Dr. E.A Gopalakrishnan
3. Koopman Analysis - Prof. K.P Soman
4. Epidemiology - Mr. Barathi Ganesh H B
5. Koopman operators for power systems - Ms. Suchithra K.S
6. Video processing - Mr. Sachin Kumar S and Ms. Sikha O.K
7. Multi-resolution DMD - Ms. Neethu Mohan
8. DMD with control - Ms. Sanjanashree J.P and Ms. Athira Gopalakrishnan
9. Delay coordinates - ERA and HMM - Mr. Premjith B
10. Noise and power - Mr. Jyothish Lal G
11. Sparsity and DMD - Ms. Manjusha K, Mr. Nidhin Prabhakar T.V and Ms. Ganga Gowri B
12. DMD on non-linear observables - Prof. K.P Soman
13. Neuroscience - Ms.Pravena D
14. Financial trading - Mr. Nidhin Unnithan

1. Dr. K.P. Soman, Prabaharan Poornachandran, Sachin Kumar S and Neethu Mohan, "Convex Optimization based Signal Processing for IOT." [Upcoming Book]


2. Dr. K.P. Soman and Dr. Ramachandran K.I, "Insight into Wavelets From Theory to Practice.", Prentice-Hall India 2004.


3. Dr. K.P. Soman, Shyam Diwakar, Ajay V., "Insight into Data Mining From Theory to Practice.", Prentice-Hall India, 2006.


4. Dr. K.P. Soman, Ajay. V, Loganathan R., "Machine Learning with SVM and other Kernel Methods.",Prentice-Hall India, 2009.


5. Dr. K.P.Soman, and Ramanthan, "Digital signal and Image Processing-The Sparse Way." Elsevier Publications, 2012.


6. Dr. Deepa G., Dr. Krishnan Namboodiri, "Bioinformatics: Sequential and Structural Analysis.", Narosa Publications.


7. Dr. K.I Ramachandran., Dr. Deepa, Dr. Krishnan Namboori, "Computational Chemistry and Molecular Modelling." -Springer international.


8. "Fractals for Everyone." Online version: http://cen.amritafoss.org/downloads/ (link is external) Manu Unni, Praveen Krishnan, Dr. K. P. Soman.