# 15.8. `matrix`¶

A `matrix` is similar to a `vector` except it is two-dimensional. Instead of a length, it has two dimensions, called `numrows` and `numcols`, for “number of rows” and “number of columns.”

Each element in the matrix is indentified by two indices; one specifies the row number, the other the column number.

To create a matrix, there are four constructors:

```matrix<char> m1;
matrix<int> m2 (3, 4);
matrix<double> m3 (rows, cols, 0.0);
matrix<double> m4 (m3);
```

The first is a do-nothing constructor that makes a matrix with both dimensions 0. The second takes two integers, which are the initial number of rows and columns, in that order. The third is the same as the second, except that it takes an additional parameter that is used to initialized the elements of the matrix. The fourth is a copy constructor that takes another `matrix` as a parameter.

Just as with `vectors`, we can make `matrix`es with any type of elements (including `vector`s, and even `matrix`es).

To access the elements of a matrix, we use the `[]` operator to specify the row and column:

```m2 = 1;
m3 = 10.0 * m2;
```

If we try to access an element that is out of range, the program prints an error message and quits.

The `numrows` and `numcols` functions get the number of rows and columns. Remember that the row indices run from 0 to `numrows() -1` and the column indices run from 0 to `numcols() -1`.

The usual way to traverse a matrix is with a nested loop. This loop sets each element of the matrix to the sum of its two indices:

```for (int row=0; row < m2.numrows(); row++) {
for (int col=0; col < m2.numcols(); col++) {
m2[row][col] = row + col;
}
}
```

This loop prints each row of the matrix with tabs between the elements and newlines between the rows:

```for (int row=0; row < m2.numrows(); row++) {
for (int col=0; col < m2.numcols(); col++) {
cout << m2[row][col] << "\t";
}
cout << endl;
}
```
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