diff --git a/include/cotila/matrix/utility.h b/include/cotila/matrix/utility.h
index f4abe04..5cd42b4 100644
--- a/include/cotila/matrix/utility.h
+++ b/include/cotila/matrix/utility.h
@@ -121,8 +121,8 @@ constexpr matrix<T, N, M> fill(T value) {
 /** @brief shifts matrix elements
  *  @param m an \f$ M \times M \f$ matrix of type T
  *  @param n the amount to shift each element
- *  @return an N-vector of type T \f$ \textbf{v} \gg n \f$ such that
- *  \f$ \left(\textbf{v} \gg n\right)_i = \textbf{v}_{(i + n)\ \textrm{mod}\ N} \f$
+ *  @return an \f$ N \times M \f$ matrix of type T such that
+ *  \f$ \left(\textbf{m} \gg n\right)_{ij} = \textbf{v}_{kj} with k = (i + n)\ \textrm{mod}\ N \f$
  *
  *  Rotates a matrix by shifting its elements vertically.
  */