Theorems · Theorem · linear algebra
LinearMap.traceAux_eq
∀ (R : Type u) [inst : CommSemiring R] {M : Type v} [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {ι : Type w}
[inst_3 : DecidableEq ι] [inst_4 : Fintype ι] {κ : Type u_1} [inst_5 : DecidableEq κ] [inst_6 : Fintype κ]
(b : Module.Basis ι R M) (c : Module.Basis κ R M), LinearMap.traceAux R b = LinearMap.traceAux R c- Defined in
- Mathlib.LinearAlgebra.Trace
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- AddCommMonoidstatement and proof · cited by 12,281
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement and proof · cited by 10,215
- Fintypestatement and proof · cited by 7,736
- Matrixproof · cited by 4,303
- LinearMap.compproof · cited by 1,642
- Module.Basisstatement and proof · cited by 1,477
- LinearMap.extproof · cited by 844
- LinearMap.idproof · cited by 625
Cited by3
Results whose statement or proof uses this declaration.
- LinearMap.trace_eq_matrix_traceproof · cited by 14
- LinearMap.trace_eq_matrix_trace_of_finsetproof · cited by 1
- LinearMap.IsPositive.trace_nonnegproof · cited by 0