docs: Some doc strings for instances

HepLean/Mathematics/LinearMaps.lean

@@ -24,6 +24,7 @@ namespace HomogeneousQuadratic
 
 variable {V : Type} [AddCommMonoid V] [Module ℚ V]
 
+/-- A homogenous quadratic equation can be treated as a function from `V` to `ℚ`. -/
 instance instFun : FunLike (HomogeneousQuadratic V) V ℚ where
   coe f := f.toFun
   coe_injective' f g h := by
@@ -49,6 +50,7 @@ open BigOperators
 
 variable {V : Type} [AddCommMonoid V] [Module ℚ V]
 
+/-- A symmetric bilinear form can be treated as a function from `V` to `V →ₗ[ℚ] ℚ`. -/
 instance instFun (V : Type) [AddCommMonoid V] [Module ℚ V] :
     FunLike (BiLinearSymm V) V (V →ₗ[ℚ] ℚ) where
   coe f := f.toFun
@@ -146,6 +148,7 @@ namespace HomogeneousCubic
 
 variable {V : Type} [AddCommMonoid V] [Module ℚ V]
 
+/-- A homogenous cubic equation can be treated as a function from `V` to `ℚ`. -/
 instance instFun : FunLike (HomogeneousCubic V) V ℚ where
   coe f := f.toFun
   coe_injective' f g h := by
@@ -168,6 +171,7 @@ namespace TriLinearSymm
 open BigOperators
 variable {V : Type} [AddCommMonoid V] [Module ℚ V]
 
+/-- A symmetric trilinear form can be treated as a function from `V` to `V →ₗ[ℚ] V →ₗ[ℚ] ℚ`. -/
 instance instFun : FunLike (TriLinearSymm V) V (V →ₗ[ℚ] V →ₗ[ℚ] ℚ) where
   coe f := f.toFun
   coe_injective' f g h := by

HepLean/Mathematics/SO3/Basic.lean

@@ -19,6 +19,7 @@ open Matrix
 /-- The group of `3×3` real matrices with determinant 1 and `A * Aᵀ = 1`. -/
 def SO3 : Type := {A : Matrix (Fin 3) (Fin 3) ℝ // A.det = 1 ∧ A * Aᵀ = 1}
 
+/-- The instance of a group on `SO3`. -/
 @[simps! mul_coe one_coe inv div]
 instance SO3Group : Group SO3 where
   mul A B := ⟨A.1 * B.1,
@@ -110,6 +111,8 @@ lemma toGL_embedding : IsEmbedding toGL.toFun where
       apply And.intro (isOpen_induced hU1)
       exact hU2
 
+/-- The instance of a topological group on `SO(3)`, defined through the embedding of `SO(3)`
+  into `GL(n)`. -/
 instance : TopologicalGroup SO(3) :=
   IsInducing.topologicalGroup toGL toGL_embedding.toIsInducing