Theorems · Theorem · linear algebra
Matrix.trace_permutation
∀ {n : Type u_1} {R : Type u_2} [inst : DecidableEq n] (σ : Equiv.Perm n) [inst_1 : Fintype n]
[inst_2 : AddCommMonoidWithOne R], (Equiv.Perm.permMatrix R σ).trace = ↑(Function.fixedPoints ⇑σ).ncardThe trace of a permutation matrix equals the number of fixed points.
- Defined in
- Mathlib.LinearAlgebra.Matrix.Permutation
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
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- DFunLike.coestatement and proof · cited by 62,936
- Fintypestatement and proof · cited by 7,736
- Set.ofPredproof · cited by 6,101
- Finset.sumproof · cited by 5,195
- Finset.univproof · cited by 3,473
- Equiv.Permstatement and proof · cited by 1,375
- Finset.filterproof · cited by 949
- Set.ncardstatement and proof · cited by 344
- Matrix.tracestatement · cited by 114
- Function.fixedPointsstatement · cited by 90
- Finset.coe_filterproof · cited by 49
- AddCommMonoidWithOnestatement and proof · cited by 42
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