Theorems · Theorem · linear algebra
Matrix.charpoly_vecMulVec
∀ {R : Type u_1} [inst : CommRing R] {n : Type u_4} [inst_1 : DecidableEq n] [inst_2 : Fintype n] (u v : n → R),
(Matrix.vecMulVec u v).charpoly = Polynomial.X ^ Fintype.card n - (u ⬝ᵥ v) • Polynomial.X ^ (Fintype.card n - 1)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingDecidableEqFintype
Around this declaration
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Cites39
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Fintypestatement and proof · cited by 7,736
- Polynomialstatement and proof · cited by 5,681
- Matrixproof · cited by 4,303
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- Fintype.cardstatement and proof · cited by 1,386
- pow_zeroproof · cited by 1,094
- sub_zeroproof · cited by 938
- IsEmptyproof · cited by 759
- zero_smulproof · cited by 716
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