Theorems · Definition · linear algebra
Matrix.trace
{n : Type u_3} → {R : Type u_6} → [Fintype n] → [AddCommMonoid R] → Matrix n n R → RThe trace of a square matrix. For more bundled versions, see:
* Matrix.traceAddMonoidHom
* Matrix.traceLinearMap
- Defined in
- Mathlib.LinearAlgebra.Matrix.Trace
- Cited by
- 114 results in Mathlib
- Foundations
- Depth 14 from the axioms, rests on 93 definitions · uses propext, Quot.sound
- Assumes
- FintypeAddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Finset.univproof · cited by 3,473
- Matrix.diagproof · cited by 61
Cited by117
Results whose statement or proof uses this declaration.
- LinearMap.trace_eq_matrix_tracestatement and proof · cited by 14
- Matrix.trace_fin_twostatement · cited by 13
- Matrix.discr_fin_twostatement · cited by 12
- Algebra.trace_eq_matrix_tracestatement and proof · cited by 9
- LinearMap.trace_mul_commproof · cited by 8
- Matrix.trace_eq_zero_of_isEmptystatement · cited by 6
- Matrix.trace_eq_neg_charpoly_coeffstatement and proof · cited by 5
- Matrix.trace_mul_commstatement and proof · cited by 5
- AddMonoidHom.map_tracestatement · cited by 4
- Algebra.trace_localizationproof · cited by 4
- Matrix.traceAddMonoidHomproof · cited by 4
- Matrix.trace_negstatement · cited by 4