Theorems · Theorem · linear algebra
Matrix.vecMul_surjective_iff_isUnit
∀ {m : Type u} [inst : DecidableEq m] {R : Type u_2} [inst_1 : CommRing R] [inst_2 : Fintype m] {A : Matrix m m R},
(Function.Surjective fun v => Matrix.vecMul v A) ↔ IsUnit A- Cited by
- 2 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqCommRingFintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- IsUnitstatement and proof · cited by 1,602
- Matrix.vecMulstatement · cited by 148
- isUnit_iff_exists_inv'proof · cited by 8
- Matrix.vecMul_surjective_iff_exists_left_inverseproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Matrix.vecMul_injective_iff_isUnitproof · cited by 3
- Matrix.vecMul_surjective_of_invertibleproof · cited by 0