Theorems · Theorem · linear algebra
Matrix.trace_eq_zero_of_isEmpty
∀ {n : Type u_3} {R : Type u_6} [inst : Fintype n] [inst_1 : AddCommMonoid R] [IsEmpty n] (A : Matrix n n R),
A.trace = 0- Defined in
- Mathlib.LinearAlgebra.Matrix.Trace
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FintypeAddCommMonoidIsEmpty
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommMonoidstatement and proof · cited by 12,281
- Fintypestatement and proof · cited by 7,736
- Finset.sumproof · cited by 5,195
- Matrixstatement and proof · cited by 4,303
- IsEmptystatement and proof · cited by 759
- Matrix.tracestatement · cited by 114
- Finset.univ_eq_emptyproof · cited by 51
Cited by6
Results whose statement or proof uses this declaration.
- Matrix.trace_eq_sum_roots_charpoly_of_splitsproof · cited by 3
- Matrix.isNilpotent_trace_of_isNilpotentproof · cited by 3
- Matrix.derivative_det_one_add_X_smul_auxproof · cited by 1
- Matrix.trace_eq_neg_charpoly_nextCoeffproof · cited by 1
- Matrix.coeff_charpolyRev_eq_neg_traceproof · cited by 1
- Matrix.trace_map'proof · cited by 0