diff --git a/Eigen/src/Core/SolveTriangular.h b/Eigen/src/Core/SolveTriangular.h
index 049890b25..4652e2e19 100644
--- a/Eigen/src/Core/SolveTriangular.h
+++ b/Eigen/src/Core/SolveTriangular.h
@@ -169,6 +169,9 @@ void TriangularViewImpl<MatrixType,Mode,Dense>::solveInPlace(const MatrixBase<Ot
   OtherDerived& other = _other.const_cast_derived();
   eigen_assert( derived().cols() == derived().rows() && ((Side==OnTheLeft && derived().cols() == other.rows()) || (Side==OnTheRight && derived().cols() == other.cols())) );
   eigen_assert((!(Mode & ZeroDiag)) && bool(Mode & (Upper|Lower)));
+  // If solving for a 0x0 matrix, nothing to do, simply return.
+  if (derived().cols() == 0)
+    return;
 
   enum { copy = (internal::traits<OtherDerived>::Flags & RowMajorBit)  && OtherDerived::IsVectorAtCompileTime && OtherDerived::SizeAtCompileTime!=1};
   typedef typename internal::conditional<copy,
diff --git a/test/lu.cpp b/test/lu.cpp
index cad703dd0..7c3872b40 100644
--- a/test/lu.cpp
+++ b/test/lu.cpp
@@ -57,6 +57,10 @@ template<typename MatrixType> void lu_non_invertible()
   // The image of the zero matrix should consist of a single (zero) column vector
   VERIFY((MatrixType::Zero(rows,cols).fullPivLu().image(MatrixType::Zero(rows,cols)).cols() == 1));
 
+  // The kernel of the zero matrix is the entire space, and thus is an invertible matrix of dimensions cols.
+  KernelMatrixType kernel = MatrixType::Zero(rows,cols).fullPivLu().kernel();
+  VERIFY((kernel.fullPivLu().isInvertible()));
+
   MatrixType m1(rows, cols), m3(rows, cols2);
   CMatrixType m2(cols, cols2);
   createRandomPIMatrixOfRank(rank, rows, cols, m1);