Quadratic Form in Linear Algebra An expression is called quadratic form in the variables x1, x2, x3,………….,xn over field F. Where aij i=1,2,3,….n, j=1,2,3,….m are elements of F. If aij are real then quadratic form is called real quadratic form. Examples of Quadratic Form 1-x12+x22+ 6 x1 x2 is a quadratic form in variables x1

To understand test for  convergence of a series you have to understand sequence and series and related concepts. Sequence A sequence S is a function whose domain is natural numbers and range is real numbers. i.e S: N->R. It is common practice to write a sequence S as Sn Examples of Sequences- Sn = <2n+1>

If z is a function of two independent variables x and y. Then second order partial differential equation Rr+Ss+Tt+ f(x,y,z,p,q)=0 Where r, s and t are and R, S and T are continuous functions of x and y in domain of xy-plane. Then if S2-4RT > 0 Then equation is hyperbolic S2-4RT= 0 Then equation

Matrix Representation of a Linear Transformation Suppose U and V are two vector spaces over the same field F of dimensions m and n. Let A = {α1, α2, α 3,……,α3} and B={β1, β2, β3,…….,βn} be ordered bases of U and V. If T is a linear transformation such that T:U->V and it is defined

Bubble Sort in Python The basic idea behind bubble sort is to compare the first element in list to second element . Compare the second element to the third element if greater swap the elements. Compare the third element to the fourth element if greater swap the elements. Do until the list is sorted. The

To  understand  Caley-Hamilton theorem you have to know about characteristic polynomial. Characteristic Polynomial If A is a square matrix of of size n * n, and I is identity matrix of the same size as A. Then determinant |A-λI| will result in an equation of the form. Which is called characteristic equation of matrix A

Hyperbolic Functions These functions are very important in regression, classification and to build neural networks. Moreover, it is important to remember expression hyperbolic functions in the form of exponential functions. I have written the expressions and plotted the functions using python library. Python Codes to Plot Hyperbolic Functions import numpy as np import matplotlib.pyplot as

Basics of Python : Calculate Factorial   Python is popular and easy to use language. It is widely used in data science, machine learning, Internet of Things (IoT)  and field of automation  However, it is necessary to learn basics to manipulate statements and customize programs. In this post, I will make a simple factorial program

Linear regression Linear regression refers to find out degree of relationship between two variables in the form of a linear function y=mx+c using statistical techniques. Where m is gradient and c is intercept on y axis. That best fits the data set, which predicts the value of y for a given x or vice versa.

For large value of n binomial distribution asymptotically tends to Poisson distribution. Probability distribution  function of binomial random variable  is Probability distribution of Poisson random variable is Poisson Distribution as a Limiting Case of Binomial Distribution Python Code for Binomial Distribution from scipy.stats import binom import numpy as np import matplotlib.pyplot as plt # Let