Theorems · Theorem · linear algebra
Matrix.isHermitian_map_iff
∀ {α : Type u_1} {β : Type u_2} {n : Type u_4} [inst : Star α] [inst_1 : Star β] {A : Matrix n n α} {f : α → β},
Function.Semiconj f star star → Function.Injective f → ((A.map f).IsHermitian ↔ A.IsHermitian)- Defined in
- Mathlib.LinearAlgebra.Matrix.Hermitian
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- 0 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Quot.sound
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Matrixstatement and proof · cited by 4,303
- Star.starstatement and proof · cited by 1,082
- Starstatement and proof · cited by 496
- Matrix.mapstatement and proof · cited by 247
- Matrix.conjTransposeproof · cited by 202
- Matrix.IsHermitianstatement and proof · cited by 126
- Function.Semiconjstatement and proof · cited by 82
- Matrix.map_injectiveproof · cited by 5
- Matrix.conjTranspose_mapproof · cited by 2
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