Apply suggestions from code review

Co-authored-by: Mateusz Baran <[email protected]>

src/manifolds/MetricManifold.jl

@@ -54,7 +54,7 @@ abstract type RiemannianMetric <: AbstractMetric end
 @doc raw"""
     change_gradient(M::AbstractManifold, G2::AbstractMetric, p, X)
 
-Convert the gradint `X` at `p` on the[`AbstractManifold`](@ref) `M` from one metric to another.
+Convert the gradient `X` at `p` on the[`AbstractManifold`](@ref) `M` from one metric to another.
 
 Assume that for a real-valued function ``f: \mathcal M \to ℝ`` we are given the Riesz representer of the differential with respect to the metric ``g_2`` i.e.
 
@@ -78,7 +78,7 @@ the same basis of the tangent space, the equation reads
 ```
 where `\cdot^*`` denotes the conjugate transpose.
 
-and we obtain `c(x) = (G_1\backslask G_2)^*x `
+and we obtain ``c(X) = (G_1\backslash G_2)^*X``
 
 # Examples
 
@@ -90,7 +90,7 @@ Since the metric in ``T_p\mathbb S^2`` is the Euclidean metric from the embeddin
 
 Here, the default metric in `\mathcal P(3)` is the [`LinearAffineMetric`](@ref) and the transformation can be computed as ``pXp``
 """
-change_tangent(::AbstractManifold, ::AbstractMetric, ::Any, ::Any)
+change_gradient(::AbstractManifold, ::AbstractMetric, ::Any, ::Any)
 
 function change_tangent(M::AbstractManifold, G::AbstractMetric, p, X)
     if is_default_metric(M, G)