Matrix concept

A matrix is a two-dimensional, rectangular structure of elements of the same type.
The elements can be accessed by their two-dimensional position (row, column).
The rows and columns of the matrix might additionally be named and consequently can be also accessed by a pair (rowname, colname).

Create a matrix

A matrix can be manually created from a vector.
Depending on the arguments, elements are put to the matrix in a different order:

m <- matrix( 1:6, nrow = 2 );
m
     [,1] [,2] [,3]
[1,]    1    3    5
[2,]    2    4    6
m <- matrix( 1:6, nrow = 2, byrow = TRUE );
m
     [,1] [,2] [,3]
[1,]    1    2    3
[2,]    4    5    6
m <- matrix( 1:6, ncol = 2 );
m
     [,1] [,2]
[1,]    1    4
[2,]    2    5
[3,]    3    6

Test the class of m:

class( m )
[1] "matrix" "array"

Try the function str to get a compact summary of matrix content:

str( m )
 int [1:3, 1:2] 1 2 3 4 5 6

Dimensions

There are several functions to get dimensions of a matrix.

Number of columns is provided by:

ncol( m )
[1] 2

Number of rows is provided by:

nrow( m )
[1] 3

Dimensions (two elements: number of rows and number of columns):

dim( m )
[1] 3 2

Names of the columns and rows

colnames( m ) and rownames( m ) are used to set and get the vectors with columns and rows names.

Try to set the names:

m
     [,1] [,2]
[1,]    1    4
[2,]    2    5
[3,]    3    6
colnames( m ) <- c( "A", "B" )
m
     A B
[1,] 1 4
[2,] 2 5
[3,] 3 6
rownames( m ) <- c( "X", "Y", "Z" )
m
  A B
X 1 4
Y 2 5
Z 3 6

To get the names use:

rownames( m )
[1] "X" "Y" "Z"
colnames( m )
[1] "A" "B"

Accessing matrix elements

Use single brackets notation with two arguments [ row(s), col(s) ] to get/set elements.
Note, when getting only a single row or a single column the result is returned as a vector, not matrix.

m[ 3, 1 ]             # a single element as a vector
[1] 3
m[ 3, ]               # a single row as a vector
A B 
3 6 
m[ , 1 ]              # a single column as a vector
X Y Z 
1 2 3 
m[ c( 2, 3 ), 1 ]     # two rows/one column, still a vector
Y Z 
2 3 
m[ c( 2, 3 ), c( "B", "A" ) ]     # a matrix
  B A
Y 5 2
Z 6 3
m[ c( F, T, T ), c( "B", "A" ) ]  # a matrix
  B A
Y 5 2
Z 6 3

Notice the difference in the output class when only a single element is requested:

class( m[ 3, 1 ] )
[1] "integer"
class( m[ c( 2, 3 ), c( "B", "A" ) ] )
[1] "matrix" "array"

With the drop argument you may enforce that always a matrix is returned (never a vector):

m[ 3, 1 ]                 # a vector
[1] 3
m[ 3, 1, drop = FALSE ]   # a matrix
  A
Z 3
class( m[ 3, 1, drop = FALSE ] )
[1] "matrix" "array"

Empty row/column argument field means all rows and/or all columns:

m[ , c( "B", "A" ) ]       # all rows, selected columns
  B A
X 4 1
Y 5 2
Z 6 3
m[ c( "Z", "X", "Y" ), ]   # selected rows, all columns
  A B
Z 3 6
X 1 4
Y 2 5
m[ , ]                     # all rows and columns, same as just "m"
  A B
X 1 4
Y 2 5
Z 3 6

Useful matrix functions

Short summary of matrix operations: http://www.statmethods.net/advstats/matrix.html

Transposition

m <- matrix( 1:6, nrow = 3 );
colnames( m ) <- c( "A", "B" )
rownames( m ) <- c( "X", "Y", "Z" )
m
  A B
X 1 4
Y 2 5
Z 3 6
t(m)
  X Y Z
A 1 2 3
B 4 5 6

Matrix multiplication

m
  A B
X 1 4
Y 2 5
Z 3 6
t( m )
  X Y Z
A 1 2 3
B 4 5 6
m %*% t( m )
   X  Y  Z
X 17 22 27
Y 22 29 36
Z 27 36 45

Element-wise multiplication

m
  A B
X 1 4
Y 2 5
Z 3 6
m+1
  A B
X 2 5
Y 3 6
Z 4 7
m * (m+1)
   A  B
X  2 20
Y  6 30
Z 12 42

Row/columns means/sums

m
  A B
X 1 4
Y 2 5
Z 3 6
rowMeans( m )
  X   Y   Z 
2.5 3.5 4.5 
rowSums( m )
X Y Z 
5 7 9 
colMeans( m )
A B 
2 5 
colSums( m )
 A  B 
 6 15

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