# Math-Linux.com

Knowledge base dedicated to Linux and applied mathematics.

# Most recent articles

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

9 May, by

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

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

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

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

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

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

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

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

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

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

### Latex convolution symbol

13 February, by

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

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

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

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 »

7 February, by

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

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

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

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

2 February, by

### Derivative of tan x

23 January, by

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 »