English
Given a vector x in M and a linear form f on M, the endomorphism defined by y ↦ y − f(y)·x is introduced as preReflection.
Русский
Задан вектор x в M и линейная форма f на M; градационная сама отображение y ↦ y − f(y)·x задаёт отображение предрев reflection.
LaTeX
$$\text{preReflection} : End_R(M) := \text{LinearMap.id} - f.smulRight x$$
Lean4
/-- Given an element `x` in a module `M` and a linear form `f` on `M`, we define the endomorphism
of `M` for which `y ↦ y - (f y) • x`.
One is typically interested in this endomorphism when `f x = 2`; this definition exists to allow the
user defer discharging this proof obligation. See also `Module.reflection`. -/
def preReflection : End R M :=
LinearMap.id - f.smulRight x
