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Knowledge base dedicated to Linux and applied mathematics.

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A subgroup is normal if and only if it is the kernel of a homomorphism.

9 May, by Nadir Soualem

We are going tho show that the kernel of a group homomorphism is a normal subgroup. Next, we prove that every normal subgroup is the kernel of a (...) Read More »

How to write matrices in Latex ? matrix, pmatrix, bmatrix, vmatrix, Vmatrix

28 March, by Nadir Soualem

How to write matrices in Latex ? matrix, pmatrix, bmatrix, vmatrix, Vmatrix. Here are few examples to write quickly (...) Read More »

Sine is an odd function sin(-x)=-sin x

22 February, by Nadir Soualem

We prove here that the sine function sin (-x) = - sin x is odd using the unit circle. Read More »

Cosine is even function cos(-x)=cos x

22 February, by Nadir Soualem

We prove here that the cosine function cos(-x)=cos x is even using the unit circle. Read More »

Newton’s interpolation polynomial

20 February, by Nadir Soualem

In this section, we shall study the polynomial interpolation in the form of Newton. Given a sequence of (n+1) data points and a function f, the (...) Read More »

Chain rule proof - derivative of a composite function

20 February, by Nadir Soualem

Derivative of composite function (g ∘ f) (g circle f), chain rule is defined by (g ∘ f)’(x) = g’(f(x)) × f’(x) . Derivative of composite function (u ∘ (...) Read More »

Latex imaginary part symbol

15 February, by Nadir Soualem

How to write Latex imaginary part symbol of a complex number? The real number b is called the imaginary part of the complex number a + (...) Read More »

Latex real part symbol

15 February, by Nadir Soualem

How to write Latex real part symbol of a complex number? The real number a is called the real part of the complex number a + (...) Read More »

Latex tensor product

13 February, by Nadir Soualem

How to write Latex tensor product symbol ? Given two vectors v, w, we can form a tensor using the outer product, which is denoted v ⊗ (...) Read More »

Latex backslash symbol

13 February, by Nadir Soualem

Latex how to write backslash in Latex with or without amssymb : backslash , setminus, smallsetminus Read More »

Latex convolution symbol

13 February, by Nadir Soualem

How to write convolution symbol using Latex ? In function analysis, the convolution of f and g f∗g is defined as the integral of the product of (...) Read More »

Chebyshev polynomials

13 February, by Nadir Soualem

Chebyshev polynomials are a useful and important tool in the field of interpolation. Indeed, in order to minimize the error in Lagrange (...) Read More »

Latex arrows

13 February, by Nadir Soualem

How to use and define arrows symbols in latex. Latex Up and down arrows, Latex Left and right arrows, Latex Direction and Maps to arrow and Latex (...) Read More »

Latex jacobian symbol

8 February, by Nadir Soualem

How to write jacobian symbol in Latex ? The jacobian matrix of vector-valued function f is the matrix of all its first-order partial (...) Read More »

Latex gradient symbol

7 February, by Nadir Soualem

How to write gradient symbol in Latex ? The gradient of a differentiable function f of several variables is the vector field whose components are (...) Read More »

Derivative of inverse functions

7 February, by Nadir Soualem

Derivative of the inverse function f^-1 is given by : (f^-1)’(x)=1 / f’ (f^-1(x)) To prove this result, we are going to apply the Chain rule (...) Read More »

Derivative of exp x, e^x

6 February, by Nadir Soualem

Derivative f’ of the function f(x)=exp x is: f’(x) = exp x for any value of x. Read More »

Derivative of sin x

6 February, by Nadir Soualem

Derivative f’ of the function f(x)=sinx is: f’(x) = cos x for any value of x. Read More »

How to diff remote files using ssh ?

2 February, by Nadir Soualem

Read More »

Derivative of tan x

23 January, by Nadir Soualem

Derivative f’ of the function f(x)=tan x is: f’(x) = 1 + tan²x for any value x different of π/2 + kπ avec k ∈Z Read More »

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