diff --git a/Eigen/src/SparseCore/SparseColEtree.h b/Eigen/src/SparseCore/SparseColEtree.h
index f89ca3814..f8745f461 100644
--- a/Eigen/src/SparseCore/SparseColEtree.h
+++ b/Eigen/src/SparseCore/SparseColEtree.h
@@ -63,6 +63,7 @@ int coletree(const MatrixType& mat, IndexVector& parent, IndexVector& firstRowEl
   typedef typename MatrixType::Index Index;
   Index nc = mat.cols(); // Number of columns 
   Index m = mat.rows();
+  Index diagSize = (std::min)(nc,m);
   IndexVector root(nc); // root of subtree of etree 
   root.setZero();
   IndexVector pp(nc); // disjoint sets 
@@ -72,7 +73,7 @@ int coletree(const MatrixType& mat, IndexVector& parent, IndexVector& firstRowEl
   Index row,col; 
   firstRowElt.resize(m);
   firstRowElt.setConstant(nc);
-  firstRowElt.segment(0, nc).setLinSpaced(nc, 0, nc-1);
+  firstRowElt.segment(0, diagSize).setLinSpaced(diagSize, 0, diagSize-1);
   bool found_diag;
   for (col = 0; col < nc; col++)
   {
@@ -91,7 +92,7 @@ int coletree(const MatrixType& mat, IndexVector& parent, IndexVector& firstRowEl
   Index rset, cset, rroot; 
   for (col = 0; col < nc; col++) 
   {
-    found_diag = false;
+    found_diag = col>=m;
     pp(col) = col; 
     cset = col; 
     root(cset) = col; 
@@ -105,6 +106,7 @@ int coletree(const MatrixType& mat, IndexVector& parent, IndexVector& firstRowEl
       Index i = col;
       if(it) i = it.index();
       if (i == col) found_diag = true;
+      
       row = firstRowElt(i);
       if (row >= col) continue; 
       rset = internal::etree_find(row, pp); // Find the name of the set containing row
diff --git a/Eigen/src/SparseQR/SparseQR.h b/Eigen/src/SparseQR/SparseQR.h
index c42dfc556..50c4c1145 100644
--- a/Eigen/src/SparseQR/SparseQR.h
+++ b/Eigen/src/SparseQR/SparseQR.h
@@ -161,8 +161,9 @@ class SparseQR
       b = y;
       
       // Solve with the triangular matrix R
+      y.resize((std::max)(cols(),Index(y.rows())),y.cols());
       y.topRows(rank) = this->matrixR().topLeftCorner(rank, rank).template triangularView<Upper>().solve(b.topRows(rank));
-      y.bottomRows(y.size()-rank).setZero();
+      y.bottomRows(y.rows()-rank).setZero();
 
       // Apply the column permutation
       if (m_perm_c.size())  dest.topRows(cols()) = colsPermutation() * y.topRows(cols());
@@ -246,7 +247,7 @@ class SparseQR
     Index m_nonzeropivots;          // Number of non zero pivots found 
     IndexVector m_etree;            // Column elimination tree
     IndexVector m_firstRowElt;      // First element in each row
-    bool m_isQSorted;                 // whether Q is sorted or not
+    bool m_isQSorted;               // whether Q is sorted or not
     
     template <typename, typename > friend struct SparseQR_QProduct;
     template <typename > friend struct SparseQRMatrixQReturnType;
@@ -338,7 +339,7 @@ void SparseQR<MatrixType,OrderingType>::factorize(const MatrixType& mat)
   Index nonzeroCol = 0; // Record the number of valid pivots
   
   // Left looking rank-revealing QR factorization: compute a column of R and Q at a time
-  for (Index col = 0; col < n; ++col)
+  for (Index col = 0; col < (std::min)(n,m); ++col)
   {
     mark.setConstant(-1);
     m_R.startVec(col);
@@ -346,7 +347,7 @@ void SparseQR<MatrixType,OrderingType>::factorize(const MatrixType& mat)
     mark(nonzeroCol) = col;
     Qidx(0) = nonzeroCol;
     nzcolR = 0; nzcolQ = 1;
-    found_diag = false;
+    found_diag = col>=m;
     tval.setZero(); 
     
     // Symbolic factorization: find the nonzero locations of the column k of the factors R and Q, i.e.,