Theorems · Theorem · linear algebra
Matrix.charpoly_zero
∀ {R : Type u_1} [inst : CommRing R] {n : Type u_4} [inst_1 : DecidableEq n] [inst_2 : Fintype n],
Matrix.charpoly 0 = Polynomial.X ^ Fintype.card n- 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.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Fintypestatement and proof · cited by 7,736
- Polynomialstatement · cited by 5,681
- Matrixstatement · cited by 4,303
- Polynomial.Xstatement and proof · cited by 1,639
- Fintype.cardstatement and proof · cited by 1,386
- Matrix.diagonalproof · cited by 314
- Finset.prod_constproof · cited by 154
- Matrix.det.congr_simpproof · cited by 91
- Matrix.charpolystatement · cited by 82
- Matrix.charmatrixproof · cited by 42
- Matrix.det_diagonalproof · cited by 27
Cited by1
Results whose statement or proof uses this declaration.
- LinearMap.charpoly_zeroproof · cited by 0