Theorems · Theorem · linear algebra
Matrix.eq_zero_of_det_mem_nonZeroDivisors_of_mulVec_eq_zero
∀ {m : Type u_1} {R : Type u_2} [inst : CommRing R] [inst_1 : Fintype m] [inst_2 : DecidableEq m] {M : Matrix m m R},
M.det ∈ nonZeroDivisors R → ∀ {v : m → R}, M.mulVec v = 0 → v = 0- Cited by
- 1 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingFintypeDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Submonoidstatement · cited by 3,086
- nonZeroDivisorsstatement and proof · cited by 895
- Matrix.detstatement and proof · cited by 665
- Matrix.mulVecstatement and proof · cited by 267
- Matrix.Nondegenerate.separatingRightproof · cited by 4
- Matrix.Nondegenerate.of_det_mem_nonZeroDivisorsproof · cited by 3
- Matrix.SeparatingRight.eq_zero_of_mulVec_eq_zeroproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Matrix.mulVec_injective_of_det_mem_nonZeroDivisorsproof · cited by 3