Theorems · Theorem · linear algebra
Matrix.Nondegenerate.of_det_mem_nonZeroDivisors
∀ {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 → M.Nondegenerate- Cited by
- 3 results in Mathlib
- Foundations
- Depth 101 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.
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
- nonZeroDivisorsstatement and proof · cited by 895
- Matrix.detstatement and proof · cited by 665
- Matrix.det_transposeproof · cited by 51
- Matrix.Nondegeneratestatement · cited by 49
- Matrix.separatingLeft_transpose_iffproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Matrix.nondegenerate_of_det_ne_zeroproof · cited by 2
- Matrix.eq_zero_of_det_mem_nonZeroDivisors_of_mulVec_eq_zeroproof · cited by 1
- Matrix.eq_zero_of_det_mem_nonZeroDivisors_of_vecMul_eq_zeroproof · cited by 0