Theorems · Theorem · linear algebra
Matrix.trace_diagonal
∀ {R : Type u_6} [inst : AddCommMonoid R] {o : Type u_8} [inst_1 : Fintype o] [inst_2 : DecidableEq o] (d : o → R),
(Matrix.diagonal d).trace = ∑ i, d i- Defined in
- Mathlib.LinearAlgebra.Matrix.Trace
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Quot.sound
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.sumstatement and proof · cited by 5,195
- Finset.univstatement and proof · cited by 3,473
- Matrix.diagonalstatement · cited by 314
- Matrix.tracestatement · cited by 114
- Matrix.diagonal_apply_eqproof · cited by 64
Cited by3
Results whose statement or proof uses this declaration.
- RootPairing.GeckConstruction.trace_h_eq_zeroproof · cited by 1
- Matrix.isParabolic_iff_existsproof · cited by 1
- Matrix.PosSemidef.trace_eq_zero_iffproof · cited by 0