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feat(data/matrix/basic): add lemma minor_map (#8074)
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Add lemma `minor_map` proving that the operations of taking a minor and applying a map to the coefficients of a matrix commute.
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faenuccio committed Jun 24, 2021
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3 changes: 3 additions & 0 deletions src/data/matrix/basic.lean
Expand Up @@ -935,6 +935,9 @@ lemma minor_smul {R : Type*} [semiring R] [add_comm_monoid α] [module R α] (r
(A : matrix m n α) :
((r • A : matrix m n α).minor : (l → m) → (o → n) → matrix l o α) = r • A.minor := rfl

lemma minor_map (f : α → β) (e₁ : l → m) (e₂ : o → n) (A : matrix m n α) :
(A.map f).minor e₁ e₂ = (A.minor e₁ e₂).map f := rfl

/-- Given a `(m × m)` diagonal matrix defined by a map `d : m → α`, if the reindexing map `e` is
injective, then the resulting matrix is again diagonal. -/
lemma minor_diagonal [has_zero α] [decidable_eq m] [decidable_eq l] (d : m → α) (e : l → m)
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