Theorems · Theorem · ring theory

invariantBasisNumber_iff_matrix

∀ {R : Type u_1} [inst : Semiring R],
  InvariantBasisNumber R ↔
    ∀ (n m : ℕ) (f : Matrix (Fin n) (Fin m) R) (g : Matrix (Fin m) (Fin n) R), f * g = 1 → g * f = 1 → n = m

Defined in

Mathlib.LinearAlgebra.Matrix.InvariantBasisNumber

Cited by

0 results in Mathlib

Foundations

Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

Semiring