Variable Declaration and Definition in Python Unlike C/C++ and Java, Python uses dynamic typed variables. What does it mean? To know answer of the question see the variable declaration in C. int x; It means you declare a variable x then compiler allocates memory and assigns a garbage value to x. You can initialize […]

List in Python List in Python is a very powerful data structure which can store any type of data which is supported by Python. It is created using square bracket for example l=[2,4,5.2,’post’,’network’,10] this statement creates a list object of class list, and indexes objects as l[0], l[1], l[2], l[3], l[4] and l[5]. If you

Sets Set is a collection of well-defined objects. Set’s Representation Basically, there are two ways of a set representation. Types of Set 1-Null Set A set is called null set if it is empty or it does not have any elements and it is denoted by fi. 2-Singelton Set A set is called singleton if

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