Theorems · Theorem · linear algebra
Matrix.Nondegenerate.smul_iff
∀ {n : Type u_1} {A : Type u_4} [inst : CommRing A] [IsDomain A] {M : Matrix n n A} [inst_2 : Finite n] {t : A},
t ≠ 0 → ((t • M).Nondegenerate ↔ M.Nondegenerate)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Fintypeproof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- Finitestatement and proof · cited by 3,029
- IsDomainstatement and proof · cited by 2,196
- Matrix.mulVecproof · cited by 267
- Fintype.ofFiniteproof · cited by 255
- dotProductproof · cited by 194
- Matrix.Nondegeneratestatement and proof · cited by 49
- Matrix.smul_mulVecproof · cited by 5
- dotProduct_smulproof · cited by 4
- Matrix.nondegenerate_defproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- RootPairing.Base.cartanMatrixIn_nondegenerateproof · cited by 1