A matrix with only one column is called a *column vector*,
or simply a *vector*.
For example,
and
are vectors.
Then we can define the addition ``
''
of two vectors,
and the multiplications ``
'' of a vector
with a real number , in which
is called a *scalar*.
For example,

and

In Matlab/Octave we can set a new vector in either of the following forms:

> u = [1; -2; -5] > u = [1 -2 -5]'If you type only ``

> u + v > 5 * u

EXAMPLE 1. Given and , find , , and .

The following vectors and are called a 2-dimensional and 3-dimensional vector, respectively.

and in general.

A vector
with real numbers
is called an

Department of Mathematics