Docs updates (#131)

readme.md

@@ -10,7 +10,7 @@ The Arnoldi Method with Krylov-Schur restart, natively in Julia.
 [![Stable docs](https://img.shields.io/badge/docs-stable-blue.svg)](https://julialinearalgebra.github.io/ArnoldiMethod.jl/stable) [![Latest docs](https://img.shields.io/badge/docs-dev-blue.svg)](https://julialinearalgebra.github.io/ArnoldiMethod.jl/dev)
 
 ## Goal
-Make `eigs` a native Julia function.
+Make `eigs` an efficient and native Julia function.
 
 ## Installation
 

src/eigvals.jl

@@ -71,9 +71,13 @@ Transforms a partial Schur decomposition into an eigendecomposition.
 
 !!! note
 
-    For real-symmetric and Hermitian matrices the Schur vectors coincide with 
-    the eigenvectors, and hence it is not necessary to call this function in 
-    that case.
+    For real-symmetric and complex-Hermitian matrices the Schur vectors coincide with
+    the eigenvectors and the R matrix is diagonal, and hence it is not necessary to call
+    this function in that case.
+
+    In fact, in case of real-symmetric and complex-Hermitian matrices *with repeated
+    eigenvalues*, calling `partialeigen` may be undesirable, as it can return eigenvectors
+    that are not orthogonal. The Schur vectors on the other hand are orthogonal by construction.
 
 The method still relies on LAPACK to compute the eigenvectors of the (quasi)
 upper triangular matrix `R` from the partial Schur decomposition.