English
The repr map provides a way to express any vector in the span as a linear combination of the independent vectors.
Русский
Каркасная отображение repr даёт способ выразить любой вектор в покрытии как линейную комбинацию независимых векторов.
LaTeX
$$repr : span_R(range v) →_lin_R (ι →_0 R)$$
Lean4
/-- Linear combination representing a vector in the span of linearly independent vectors.
Given a family of linearly independent vectors, we can represent any vector in their span as
a linear combination of these vectors. These are provided by this linear map.
It is simply one direction of `LinearIndependent.linearCombinationEquiv`. -/
def repr (hv : LinearIndependent R v) : span R (range v) →ₗ[R] ι →₀ R :=
hv.linearCombinationEquiv.symm
