Theorems · Theorem · linear algebra
Matrix.charpoly_of_isUpperTriangular
∀ {R : Type u_1} [inst : CommRing R] {n : Type u_4} [inst_1 : DecidableEq n] [inst_2 : Fintype n]
[inst_3 : LinearOrder n] (M : Matrix n n R),
M.IsUpperTriangular → M.charpoly = ∏ i, (Polynomial.X - Polynomial.C (M i i))- Cited by
- 1 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- RingHomstatement · cited by 10,189
- LinearOrderstatement and proof · cited by 8,572
- Fintypestatement and proof · cited by 7,736
- Polynomialstatement · cited by 5,681
- Matrixstatement and proof · cited by 4,303
- Finset.univstatement and proof · cited by 3,473
- Finset.prodstatement and proof · cited by 2,356
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.Cstatement and proof · cited by 1,598
- Finset.prod_congrproof · cited by 646
Cited by1
Results whose statement or proof uses this declaration.
- Matrix.charpoly_of_upperTriangularproof · cited by 0