Theorems · Theorem · linear algebra
Matrix.isNilpotent_trace_of_isNilpotent
∀ {R : Type u} [inst : CommRing R] {n : Type v} [inst_1 : DecidableEq n] [inst_2 : Fintype n] {M : Matrix n n R},
IsNilpotent M → IsNilpotent M.trace- Cited by
- 3 results in Mathlib
- Foundations
- Depth 119 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.
Cites14
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
- Matrixstatement and proof · cited by 4,303
- Polynomial.coeffproof · cited by 1,045
- one_ne_zeroproof · cited by 885
- IsEmptyproof · cited by 759
- isEmpty_or_nonemptyproof · cited by 269
- IsNilpotentstatement and proof · cited by 248
- Matrix.tracestatement · cited by 114
- Matrix.charpolyRevproof · cited by 9
- Matrix.trace_eq_zero_of_isEmptyproof · cited by 6
- Matrix.isUnit_charpolyRev_of_isNilpotentproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- LinearMap.isNilpotent_trace_of_isNilpotentproof · cited by 5
- Matrix.isParabolic_iff_existsproof · cited by 1
- RootPairing.GeckConstruction.trace_toEnd_eq_zeroproof · cited by 0