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
of the matrix. The number of
(horizontal) and the number of
(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
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 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 .