Theorems · Theorem · linear algebra
Matrix.isSymm_toBilin_iff_isSymm
∀ {R₁ : Type u_1} {M₁ : Type u_2} [inst : CommSemiring R₁] [inst_1 : AddCommMonoid M₁] [inst_2 : Module R₁ M₁]
{n : Type u_5} [inst_3 : Fintype n] [inst_4 : DecidableEq n] (b : Module.Basis n R₁ M₁) {M : Matrix n n R₁},
((Matrix.toBilin b) M).IsSymm ↔ M.IsSymm- Cited by
- 0 results in Mathlib
- Foundations
- Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement · cited by 10,215
- Fintypestatement and proof · cited by 7,736
- Matrixstatement and proof · cited by 4,303
- LinearEquivstatement · cited by 3,317
- Module.Basisstatement and proof · cited by 1,477
- LinearMap.BilinFormstatement · cited by 501
- Matrix.IsSymmstatement and proof · cited by 70
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