Singular Value Decomposition (SVD)
Introduction Singular Value Decomposition (SVD) is a matrix factorization technique that is widely used in linear algebra, statistics, signal processing,
Linear Algebra, YEM
Linear Algebra, YEM
Matrices of derivatives
Gradient Consider a scalar valued function $f(\text{X})$ defined on $n$ variables; that is, $f: \mathbb{R}^n \to \mathbb{R}$, where $\text{X}=(x_1,x_2,\cdots, x_n)^T$
Linear Algebra, YEM
Eigen Values and Eigen Vectors
Eigen value An eigen value of a square matrix $A = [a_{ij}]$ is a scalar $\lambda$ such that there exists
Calculus, YEM
Jacobians and Transformation
Introduction prerequisite: Elementary Function, Jacobian, Matrix Addition: Addition of two numbers in a real line is Translation $$ x \longmapsto
Distributions, YES
Probability Essentials
Introduction Probability allows us to quantify the variability in the outcome of any experiment whose exact outcome cannot be predicted
Distributions, YES
Transformation of Random Variables
Introduction In this note, we study how to find the probability distribution of functions of one or more random variables.
Distributions, YES
The Role of Parameters
Introduction In one of the previous notes, we discussed several common families of distributions. In this note, we discuss the
Sets and Functions, YEM
Elementary Functions
Introduction Preliminary Reference A large and practically important class of functions — the elementary functions — can be built from
Distributions, YES
Expectation and Moments of Univariate Distributions
Introduction Random variable characterises a random phenomenon by listing the range and the corresponding probability distribution (that is, pmf in
Distributions, YES
Generating Functions in Random Variables
Introduction A random variable X is completly described by its CDF, PDF, or PMF. But summarizing a distribution would be