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,
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 = [1 -2 -5]'', it gives a ``row'' instead of a ``column.'' Then the apostrophe (') must be attached, which does a transposition. You can add a vector and multiply it by a scalar as follows:
> u + v > 5 * u
EXAMPLE 1. Given and , find , , and .
The following vectors and are called a 2-dimensional and 3-dimensional vector, respectively.