Theorems · Theorem · linear algebra
Matrix.coeff_charpoly_mem_ideal_pow
∀ {R : Type u} [inst : CommRing R] {n : Type v} [inst_1 : DecidableEq n] [inst_2 : Fintype n] {M : Matrix n n R}
{I : Ideal R}, (∀ (i j : n), M i j ∈ I) → ∀ (k : ℕ), M.charpoly.coeff k ∈ I ^ (Fintype.card n - k)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingDecidableEqFintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites43
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
- Polynomialproof · cited by 5,681
- Finset.sumproof · cited by 5,195
- Idealstatement and proof · cited by 4,748
- Matrixstatement and proof · cited by 4,303
- mul_oneproof · cited by 3,885
- Finset.univproof · cited by 3,473
- Finset.prodproof · cited by 2,356
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
Cited by1
Results whose statement or proof uses this declaration.