pub trait Basis: FiniteDimensional + Sized {
type Bases: IntoIterator<Item = Self>;
fn canonical_basis() -> Self::Bases;
fn canonical_basis_component(index: usize) -> Option<Self> { ... }
fn i() -> Self
where
Self::N: Cmp<U0, Output = Greater>,
{ ... }
fn j() -> Self
where
Self::N: Cmp<U1, Output = Greater>,
{ ... }
fn k() -> Self
where
Self::N: Cmp<U2, Output = Greater>,
{ ... }
}Expand description
Describes the basis of a vector space.
Required Associated Types
type Bases: IntoIterator<Item = Self>
Required Methods
fn canonical_basis() -> Self::Bases
fn canonical_basis() -> Self::Bases
Gets a type that can be converted into an iterator over the canonical or standard basis vectors of the space.
Such basis vectors must only have one component set to the multiplicative identity and all other components set to the additive identity (one and zero in $\Reals$, respectively). Moreover, the set of basis vectors must contain ordered and unique elements and be of size equal to the dimensionality of the space.
For example, the set of canonical basis vectors for the real coordinate space $\Reals^3$ is:
$$ \{\hat{i},\hat{j},\hat{k}\}= \left\{ \begin{bmatrix}1\\0\\0\end{bmatrix}, \begin{bmatrix}0\\1\\0\end{bmatrix}, \begin{bmatrix}0\\0\\1\end{bmatrix} \right\} $$
Provided Methods
fn canonical_basis_component(index: usize) -> Option<Self>
Gets the canonical basis vector $\hat{i}$ that describes the $x$ axis.
Gets the canonical basis vector $\hat{j}$ that describes the $y$ axis.