# CS6015: Linear Algebra and Random Processes

## Course information

 Instructor Prashanth Wednesday 2:30pm to 3:30pm BSB 314 TAs Abhishek Monday 2:30pm to 3:30pm DON lab Hardi Tuesday 2:30pm to 3:30pm DON lab Ditty Wednesday 2:30pm to 3:30pm AIDB lab Jom Thursday 2:30pm to 3:30pm DON lab Purvi Friday 2:30pm to 3:30pm DON lab

## Course Content

### Linear Algebra

Matrices

Matrix Multiplication, Transposes, Inverses, Gaussian Elimination, factorization A=LU, rank

Vector spaces

Column and row spaces, Solving Ax=0 and Ax=b, Independence, basis, dimension, linear transformations

Orthogonality

Orthogonal vectors and subspaces, projection and least squares, Gram-Schmidt orthogonalization

Determinants

Determinant formula, cofactors, inverses and volume

Eigenvalues and Eigenvectors

Characteristic polynomial, Diagonalization, Hermitian and Unitary matrices, Spectral theorem, Change of basis

Positive definite matrices and singular value decomposition

### Random processes

Preliminaries

Events, probability, conditional probability, independence, product spaces

Random Variables

Distributions, law of averages, discrete and continuous r.v.s, random vectors, Monte Carlo simulation

Discrete Random Variables

Probability mass functions, independence, expectation, conditional expectation, sums of r.v.s

Continuous Random Variables

Probability density functions, independence, expectation, conditional expectation, functions of r.v.s, sum of r.v.s, multivariate normal distribution, sampling from a distribution

Convergence of Random Variables

Modes of convergence, Borel-Cantelli lemmas, laws of large numbers, central limit theorem, tail inequalities

* Advanced topics (if time permits)

Markov chains, minimum mean squared error estimation

• Mid-term (Linear Algebra concepts): 30%

• Final exam (Probability concepts): 30%

• Quizzes: 20% (Best 5 out of 8)

• Programming Assignments: 20%

## Target Audience

Masters (M.Tech/M.S.) and Ph.D. students

## Important Dates

Problem Sets Quizzes Tutorials Mid-Sem End-Sem
Aug 7 Aug 16 Aug 11 When: 10am to 12pm, Sep 24      Where: CS34 and CS36 When: 1pm to 4pm, Nov 15      Where: CS34 and CS36
Aug 18 Aug 28 Sep 1
Aug 25 28 Sep 5 Sep 20
Sep 11 Sep 18 Oct 13
Sep 28 Oct 6 Oct 23
Oct 10 Oct 17 Nov 10
Oct 20 Oct 27
Oct 27 Nov 3

## Textbooks

• Linear algebra and applications by Gilbert Strang

• Probability and random processes by Geoffrey Grimmett and David Stirzaker