Mathlib Map

Theorems · Theorem · linear algebra

Matrix.IsHermitian.eq

∀ {α : Type u_1} {n : Type u_4} [inst : Star α] {A : Matrix n n α}, A.IsHermitian → A.conjTranspose = A
Defined in
Mathlib.LinearAlgebra.Matrix.Hermitian
Cited by
11 results in Mathlib
Foundations
Depth 17 from the axioms · uses Quot.sound
Assumes
Star
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Matrix.IsHermitian.smul · cited by 3IsHermitian.smulMatrix.isHermitian_conjTranspose_mul_mul · cited by 3Matrix.isHermitian_conjTr…Matrix.isSymmetric_toLin_iff · cited by 2Matrix.isSymmetric_toLin_…Matrix.IsHermitian.hadamard · cited by 2IsHermitian.hadamardMatrix.IsHermitian.inv · cited by 2IsHermitian.invMatrix.IsHermitian.coe_re_apply_self · cited by 1IsHermitian.coe_re_apply_…Matrix.IsHermitian.map · cited by 1IsHermitian.mapMatrix.schur_complement_eq₁₁ · cited by 1Matrix.schur_complement_e…Matrix.isHermitian_mul_mul_conjTranspose · cited by 0Matrix.isHermitian_mul_mu…Matrix.IsHermitian.adjugate · cited by 0IsHermitian.adjugateMatrix.schur_complement_eq₂₂ · cited by 0Matrix.schur_complement_e…Matrix · cited by 4303MatrixStar · cited by 496StarMatrix.conjTranspose · cited by 202Matrix.conjTransposeMatrix.IsHermitian · cited by 126Matrix.IsHermitianIsHermitian.eqCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by11

Results whose statement or proof uses this declaration.