Theorems · Theorem · linear algebra
Matrix.charpoly_isEmpty
∀ {R : Type u_1} [inst : CommRing R] {n : Type u_4} [inst_1 : DecidableEq n] [inst_2 : Fintype n] [IsEmpty n]
{A : Matrix n n R}, A.charpoly = 1- Cited by
- 3 results in Mathlib
- Foundations
- Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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 and proof · cited by 4,303
- IsEmptystatement and proof · cited by 759
- Matrix.charpolystatement · cited by 82
- Matrix.charmatrixproof · cited by 42
- Matrix.coe_det_isEmptyproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- Matrix.trace_eq_sum_roots_charpoly_of_splitsproof · cited by 3
- Matrix.trace_eq_neg_charpoly_nextCoeffproof · cited by 1
- Matrix.charpoly_vecMulVecproof · cited by 0