Normalize a vector
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linalg::normalize(v) normalizes the vector with respect
to the 2-norm ().
The result of
linalg::normalize(v) is a
vector that has norm 1 and the same direction as
The scalar product for
a vector is implemented
by the function
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
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: Unable to 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