Normalize a vector
This functionality does not run in MATLAB.
linalg::normalize(v
)
linalg::normalize(v)
normalizes the vector
with respect
to the 2norm (
).
The result of linalg::normalize(v)
is a
vector that has norm 1 and the same direction as v
.
The scalar product
for
a vector
is implemented
by the function linalg::scalarProduct
.
The norm of a vector is computed with the function norm
, which is overloaded
for vectors. See the method "norm"
of the domain
constructor Dom::Matrix
for
details.
If the norm is an object that cannot be converted into an element
of the component ring of v
, then an error occurs
(see Example 2).
We define the following vector:
u := matrix([[1, 2]])
Then the vector of norm 1 with the same direction as u
is
given by:
linalg::normalize(u)
The following computation fails because the vector (1, 2) cannot be normalized over the rationals:
v := Dom::Matrix(Dom::Rational)([[1, 2]]): linalg::normalize(v)
Error: Cannot normalize the given vector over its component ring. [linalg::normalize]
If we define v
over the real numbers, then
we get the normalized vector of v
as follows:
w := Dom::Matrix(Dom::Real)(v): linalg::normalize(w)

A vector, i.e., an n×1 or 1
×n matrix of
a domain of category 
Vector of the same domain type as v
.