Theorems · Definition · linear algebra

Module.Basis.coord

{ι : Type u_10} →
  {R : Type u_11} →
    {M : Type u_12} →
      [inst : Semiring R] → [inst_1 : AddCommMonoid M] → [inst_2 : Module R M] → Module.Basis ι R M → ι → M →ₗ[R] R

b.coord i is the linear function giving the i-th coordinate of a vector with respect to the basis b. b.coord i is an element of the dual space. In particular, for finite-dimensional spaces it is the ιth basis vector of the dual space.

Defined in

Mathlib.LinearAlgebra.Basis.Defs

Cited by

64 results in Mathlib

Foundations

Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModule