Theorems · Theorem · ring theory
IsSelfAdjoint.smul
∀ {R : Type u_1} {A : Type u_2} [inst : Star R] [inst_1 : Star A] [inst_2 : SMul R A] [StarModule R A] {r : R},
IsSelfAdjoint r → ∀ {x : A}, IsSelfAdjoint x → IsSelfAdjoint (r • x)- Defined in
- Mathlib.Algebra.Star.SelfAdjoint
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses propext
- Assumes
- StarStarSMulStarModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- StarModulestatement and proof · cited by 570
- IsSelfAdjointstatement and proof · cited by 545
- Starstatement and proof · cited by 496
- IsSelfAdjoint.star_eqproof · cited by 58
- StarModule.star_smulproof · cited by 34
Cited by7
Results whose statement or proof uses this declaration.
- IsSelfAdjoint.smul_iffproof · cited by 1
- Unitization.convexOn_of_convexOn_inr_compproof · cited by 1
- CStarAlgebra.star_left_conjugate_le_norm_smulproof · cited by 1
- spectrum_star_mul_self_nonnegproof · cited by 1
- Matrix.PosDef.smulproof · cited by 1
- Unitization.concaveOn_of_concaveOn_inr_compproof · cited by 0
- Matrix.PosSemidef.smulproof · cited by 0