# Matrices

A matrix is a rectangular array of numbers enclosed by brackets.  (The plural of matrix is matrices.)

are all examples of matrices.

The numbers in a matrix are called the elements (or entries) of the matrix.  The number of rows (horizontal) and the number of columns (vertical) determine the dimensions of the matrix.  You always write the number of rows first and the number of columns second.  In order, the dimensions of the above matrices are 3 × 2 (read 3 by 2), 1 × 3, 3 × 1
and 2 × 2.

A matrix with only one row (the second one above) is called a row matrix.  If the matrix has only one column (the third one above) is a column matrix.  The last matrix above is a square matrix because the number of rows equals the number of columns.

If all of the elements of a matrix are zero, it is called a zero matrix.

is a 2 × 3 zero matrix, denoted .

One common use of matrices is for solving systems of linear equations. For this, you need to know about matrix row operations and the identity matrix.

You can also do algebra with matrices -- that is, you can add them and subtract them, multiply them (if their dimensions are compatible), and even do a sort of division by finding their inverses (this only works for square matrices). In advanced mathematics, matrices are used to describe linear transformations.