Theorems · Theorem · linear algebra
Matrix.IsHermitian.smul
∀ {α : Type u_1} {n : Type u_4} {R : Type u_5} [inst : Star R] [inst_1 : Star α] [inst_2 : SMul R α] [StarModule R α]
{A : Matrix n n α}, A.IsHermitian → ∀ {k : R}, IsSelfAdjoint k → (k • A).IsHermitian- Defined in
- Mathlib.LinearAlgebra.Matrix.Hermitian
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Quot.sound
- Assumes
- StarStarSMulStarModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- StarModulestatement and proof · cited by 570
- IsSelfAdjointstatement and proof · cited by 545
- Starstatement and proof · cited by 496
- Matrix.conjTransposeproof · cited by 202
- Matrix.IsHermitianstatement and proof · cited by 126
- IsSelfAdjoint.star_eqproof · cited by 58
- Matrix.IsHermitian.eqproof · cited by 11
- Matrix.conjTranspose_smulproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- Matrix.posSemidef_opNorm_smul_gram_sub_gramproof · cited by 0
- Matrix.IsHermitian.of_smul'proof · cited by 0
- Matrix.isHermitian_smul_iffproof · cited by 0