Theorems · Theorem · linear algebra
Matrix.charpoly_inv
∀ {R : Type u} [inst : CommRing R] {n : Type v} [inst_1 : DecidableEq n] [inst_2 : Fintype n] (A : Matrix n n R),
IsUnit A → A⁻¹.charpoly = (-1) ^ Fintype.card n * Polynomial.C (Ring.inverse A.det) * A.charpolyRev- Cited by
- 0 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingDecidableEqFintype
Around this declaration
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Cites38
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
- Fintypestatement and proof · cited by 7,736
- Polynomialstatement and proof · cited by 5,681
- Matrixstatement and proof · cited by 4,303
- one_mulproof · cited by 2,841
- Polynomial.Xproof · cited by 1,639
- map_zeroproof · cited by 1,614
- IsUnitstatement and proof · cited by 1,602
- Polynomial.Cstatement and proof · cited by 1,598
- Fintype.cardstatement and proof · cited by 1,386
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