Mathlib Map

Theorems · Theorem · linear algebra

Matrix.inv_eq_right_inv

∀ {n : Type u'} {α : Type v} [inst : Fintype n] [inst_1 : DecidableEq n] [inst_2 : CommRing α] {A B : Matrix n n α},
  A * B = 1 → A⁻¹ = B

If matrix A is right invertible, then its inverse equals its right inverse.

Defined in
Mathlib.LinearAlgebra.Matrix.NonsingularInverse
Cited by
4 results in Mathlib
Foundations
Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FintypeDecidableEqCommRing
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Matrix.J_inv · cited by 1Matrix.J_invMatrix.inv_kronecker · cited by 0Matrix.inv_kroneckerMatrix.right_inv_eq_left_inv · cited by 0Matrix.right_inv_eq_left_…Matrix.right_inv_eq_right_inv · cited by 0Matrix.right_inv_eq_right…CommRing · cited by 17173CommRingFintype · cited by 7736FintypeMatrix · cited by 4303MatrixMatrix.inv_eq_left_inv · cited by 9Matrix.inv_eq_left_invmul_eq_one_comm · cited by 5mul_eq_one_commMatrix.inv_eq_right_invCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by4

Results whose statement or proof uses this declaration.