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Matrices

There are several ways of making a matrix. You can create one directly like this:

```X<-matrix(c(1,0,0,0,1,0,0,0,1),nrow=3)

X

[,1]     [,2]     [,3]
[1,]     1        0        0
[2,]     0        1        0
[3,]     0        0        1```

where, by default, the numbers are entered columnwise. The class and attributes of X indicate that it is a matrix of three rows and three columns (these are its dim attributes)

```class(X)

  "matrix"

attributes(X)

\$dim

  3  3```

In the next example, the data in the vector appear row-wise, so we indicate this with byrow=T:

```vector<-c(1,2,3,4,4,3,2,1)
V<-matrix(vector,byrow=T,nrow=2)
V

[,1]     [,2]     [,3]     [,4]
[1,]    1        2        3        4
[2,]    4        3        2        1```

Another way to convert a vector into a matrix is by providing the vector object with two dimensions (rows and columns) using the dim function like this:

`dim(vector)<-c(4,2)`

We can check that vector has now become a matrix:

```is.matrix(vector)

 TRUE```

We need to be careful, however, because we have made no allowance at this stage for the fact that the data were entered row-wise into vector:

```vector

[,1]     [,2]
[1,]    1        4
[2,]    2        3
[3,]    3        2
[4,]    4        1```

The matrix we want is the transpose, t, of this matrix:

```(vector<-t(vector))

[,1]     [,2]     [,3]     [,4]
[1,]     1        2        3        4
[2,]     4        3        2        1```

Naming the rows and columns of matrices

At first, matrices have numbers naming their rows and columns (see above). Here is a 4 ×5 matrix of random integers from a Poisson distribution with mean= 1.5:

```X<-matrix(rpois(20,1.5),nrow=4)
X [,1] [,2] [,3] [,4] [,5] [1,] 1 0 2 5 3 [2,] 1 1 3 1 3 [3,] 3 1 0 2 2 [4,] 1 ...```

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