**Function :-**

Function are a bunch of commands grouped together in a sensible unit.

Functions take input arguments, do calculations (or make some graphics, call other functions) and produce some output and return a result in a variable. The returned variable can be a complex construct, like a list.

Syntax

Name <- function(Argument1, Argument2, ...)

{

expression

}

Where expression is a single command or a group of commands

- Function arguments can be given a meaningful name
- Function arguments can be set to default values
- Functions can have the special argument '...'

**Functions (Single variable)**

The sign <- is furthermore used for defining functions:

> abc <- function(x) {

x^2

}

> abc (3)

[1] 9

>abc (6)

[1] 36

> abc (-2)

[1] 4

**Function (Two variables)**

>abc <- function (x,y) {

x^2+y^2

}

> abc (2,3)

[1] 13

> abc (3,4)

[1] 25

> abc (-2,-1)

[1] 5

**Matrix**

- Matrices are important objects in any calculation.
- A matrix is a rectangular array with p rows and n columns.
- An element in the i-th row and j-th column is denoted by xij (book version) or x[i,j] ("program version"), i = 1,2,.....,n, j = 1,2,...,p.
- An element of a matrix can also be an object, for example a string. However, in mathematics, we are mostly interested in numerical matrices, whose element are generally real numbers

>x <- matrix (nrow = 4 , ncol = 2, data = c(1,2,3,4,5,6,7,8) )

We see:

- The parameter nrow defines the row number of a matrix.
- The parameter ncol defines the column number of a matrix.
- The parameter data assigns specified values to the matrix element.
- The value from the parameters are written column-wise in matrix.

> x

[,1] [,2]

[1,] 1 5

[2,] 2 6

[3,] 3 7

[4,] 4 8

- One can access a single element of a matrix with x[i,j] :

[1] 7

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