docs corrections

docs/src/man/eig.md

@@ -24,8 +24,8 @@ using `schursolve`.
 ```@docs
 schursolve
 ```
-Note that, for symmetric or hermitian linear maps, the eigenvalue and Schur factorizaion are
-equivalent, and one can only use `eigsolve`.
+Note that, for symmetric or hermitian linear maps, the eigenvalue and Schur factorization
+are equivalent, and one can only use `eigsolve`.
 
 Another example of a possible use case of `schursolve` is if the linear map is known to have
 a unique eigenvalue of, e.g. largest magnitude. Then, if the linear map is real valued, that

src/eigsolve/arnoldi.jl

@@ -2,8 +2,8 @@
     schursolve(A, x₀, howmany, which, algorithm)
 
 Compute a partial Schur decomposition containing `howmany` eigenvalues from the linear map
-encoded in the matrix or function `A`. Return the reduced Schur matrix, the basis of Schur vectors,
-the extracted eigenvalues and a `ConvergenceInfo` structure.
+encoded in the matrix or function `A`. Return the reduced Schur matrix, the basis of Schur
+vectors, the extracted eigenvalues and a `ConvergenceInfo` structure.
 
 See also [`eigsolve`](@eigsolve) to obtain the eigenvectors instead. For real symmetric or
 complex hermitian problems, the (partial) Schur decomposition is identical to the (partial)

src/eigsolve/geneigsolve.jl

@@ -10,10 +10,12 @@ form ``(A - λB)x = 0``, where `A` and `B` are either instances of `AbstractMatr
 function that implements the matrix vector product. In case functions are used, one could
 either specify the action of `A` and `B` via a tuple of two functions (or a function and an
 `AbstractMatrix`), or one could use a single function that takes a single argument `x` and
-returns two results, corresponding to `A*x` and `B*x`. Return eigenvalues, eigenvectors and a `ConvergenceInfo` structure.
+returns two results, corresponding to `A*x` and `B*x`. Return the computed eigenvalues,
+eigenvectors and a `ConvergenceInfo` structure.
 
 ### Arguments:
-The first argument is either a tuple of two linear maps, so a function or an `AbstractMatrix` for either of them, representing the action of `A` and `B`. Alternatively,
+The first argument is either a tuple of two linear maps, so a function or an
+`AbstractMatrix` for either of them, representing the action of `A` and `B`. Alternatively,
 a single function can be used that takes a single argument `x` and returns the equivalent of
 `(A*x, B*x)` as result. This latter form is compatible with the `do` block syntax of Julia.
 If an `AbstractMatrix` is used for either `A` or `B`, a starting vector `x₀` does not need