| import OAI.LinearAlgebra.CirculantHadamard.Model | |
| namespace OAI | |
| universe uR | |
| namespace CirculantHadamard | |
| def rowCirculant {n : ℕ} {R : Type uR} (h : Fin n → R) : | |
| Matrix (Fin n) (Fin n) R := fun i j => h (j - i) | |
| @[simp] theorem rowCirculant_apply {n : ℕ} {R : Type uR} | |
| (h : Fin n → R) (i j : Fin n) : rowCirculant h i j = h (j - i) := rfl | |
| theorem rowCirculant_isCirculant {n : ℕ} (h : Fin n → ℝ) : | |
| IsCirculant (rowCirculant h) := ⟨h, fun _ _ => rfl⟩ | |
| @[simp] theorem rowCirculant_zero_row {n : ℕ} [NeZero n] | |
| {R : Type uR} (h : Fin n → R) (j : Fin n) : rowCirculant h 0 j = h j := by | |
| simp [rowCirculant] | |
| end CirculantHadamard | |
| end OAI | |