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Theorems · Theorem · linear algebra

Matrix.circulant_isSymm_iff

∀ {α : Type u_1} {n : Type u_3} [inst : SubtractionMonoid n] {v : n → α},
  (Matrix.circulant v).IsSymm ↔ ∀ (i : n), v (-i) = v i

A circulant of v is symmetric iff v equals its reverse.

Defined in
Mathlib.LinearAlgebra.Matrix.Circulant
Cited by
2 results in Mathlib
Foundations
Depth 18 from the axioms · uses propext, Quot.sound
Assumes
SubtractionMonoid
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Matrix.Fin.circulant_isSymm_iff · cited by 1Fin.circulant_isSymm_iffMatrix.circulant_isSymm_apply · cited by 0Matrix.circulant_isSymm_a…Matrix · cited by 4303MatrixSubtractionMonoid · cited by 208SubtractionMonoidMatrix.IsSymm · cited by 70Matrix.IsSymmMatrix.circulant · cited by 27Matrix.circulantMatrix.transpose_circulant · cited by 2Matrix.transpose_circulantMatrix.circulant_inj · cited by 1Matrix.circulant_injMatrix.circulant_isSymm_iffCITED BYCITES

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Cited by2

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