Theorems · Theorem · linear algebra
Matrix.nonsingular_iff_det_mem_nonZeroDivisors
∀ {n : Type u_3} [inst : Fintype n] [inst_1 : DecidableEq n] {R : Type u_4} [inst_2 : CommRing R] {A : Matrix n n R},
A.Nonsingular ↔ A.det ∈ nonZeroDivisors R- Defined in
- Mathlib.LinearAlgebra.Matrix.Nonsingular
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeDecidableEqCommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- sub_zeroproof · cited by 938
- nonZeroDivisorsstatement and proof · cited by 895
- Matrix.detstatement and proof · cited by 665
- sub_eq_zeroproof · cited by 407
- Matrix.Nonsingularstatement · cited by 27
Cited by1
Results whose statement or proof uses this declaration.
- Matrix.nonsingular_iff_det_ne_zeroproof · cited by 0