Matrix in R

creating a Matrix

##using Vectors and cbind() and rbind()
xr1 <- c( 6, 2, 10)
xr2 <- c(1, 3, -2)
x <- rbind(xr1, xr2) ## binds the vectors into rows of a matrix
x

##     [,1] [,2] [,3]
## xr1    6    2   10
## xr2    1    3   -2

y <- cbind(xr1, xr2) ## binds the same vectors into columns of a matrix
y

##      xr1 xr2
## [1,]   6   1
## [2,]   2   3
## [3,]  10  -2

x[2,1]##The elements in a matrix are indexed by their (Row, Column) positions

## xr2 
##   1

## using vector and dim()
my.vector<- 1:12
dim(my.vector) <- c(3,4) 
my.vector

##      [,1] [,2] [,3] [,4]
## [1,]    1    4    7   10
## [2,]    2    5    8   11
## [3,]    3    6    9   12

dim(my.vector)

## [1] 3 4

## Using array() and dim attribute
my.array<- array(1:12, dim=c(3,4))
my.array

##      [,1] [,2] [,3] [,4]
## [1,]    1    4    7   10
## [2,]    2    5    8   11
## [3,]    3    6    9   12

dim(my.array)## To get the dimensions of a matrix using dim()

## [1] 3 4

## using matrix() function
A <- matrix(c( 6, 1, 0, -3, -1, 2),3, 2, byrow = TRUE)
B <- matrix(c( 4, 2, 0, 1, -5, -1),3, 2, byrow = TRUE)
A

##      [,1] [,2]
## [1,]    6    1
## [2,]    0   -3
## [3,]   -1    2

##      [,1] [,2]
## [1,]    4    2
## [2,]    0    1
## [3,]   -5   -1

##Matrix addition
 A + B

##      [,1] [,2]
## [1,]   10    3
## [2,]    0   -2
## [3,]   -6    1

##Matrix subtraction
A - B

##      [,1] [,2]
## [1,]    2   -1
## [2,]    0   -4
## [3,]    4    3

## Element-by-element matrix multiplication, not matrix multiplication

A * B

##      [,1] [,2]
## [1,]   24    2
## [2,]    0   -3
## [3,]    5   -2

## Transpose of a Matrix
t(A)

##      [,1] [,2] [,3]
## [1,]    6    0   -1
## [2,]    1   -3    2