Theorems · Theorem · linear algebra
Matrix.charpoly_of_upperTriangular
Deprecated since 2026-07-30Use Matrix.charpoly_of_isUpperTriangular instead.
∀ {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))Alias of Matrix.charpoly_of_isUpperTriangular.
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- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
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- DFunLike.coestatement · cited by 62,936
- CommRingstatement · cited by 17,173
- RingHomstatement · cited by 10,189
- LinearOrderstatement · cited by 8,572
- Fintypestatement · cited by 7,736
- Polynomialstatement · cited by 5,681
- Matrixstatement · cited by 4,303
- Finset.univstatement · cited by 3,473
- Finset.prodstatement · cited by 2,356
- Polynomial.Xstatement · cited by 1,639
- Polynomial.Cstatement · cited by 1,598
- Matrix.charpolystatement · cited by 82
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