diff --git a/GPy/kern/__init__.py b/GPy/kern/__init__.py
index 0e265a64..55b69bd7 100644
--- a/GPy/kern/__init__.py
+++ b/GPy/kern/__init__.py
@@ -1,6 +1,6 @@
 from _src.kern import Kern
 from _src.rbf import RBF
-from _src.linear import Linear
+from _src.linear import Linear, LinearFull
 from _src.static import Bias, White
 from _src.brownian import Brownian
 from _src.sympykern import Sympykern
diff --git a/GPy/kern/_src/kern.py b/GPy/kern/_src/kern.py
index 31fa8690..9d8d3f7b 100644
--- a/GPy/kern/_src/kern.py
+++ b/GPy/kern/_src/kern.py
@@ -11,7 +11,7 @@ from ...util.caching import Cache_this
 
 class Kern(Parameterized):
     #===========================================================================
-    # This adds input slice support. The rather ugly code for slicing can be 
+    # This adds input slice support. The rather ugly code for slicing can be
     # found in kernel_slice_operations
     __metaclass__ = KernCallsViaSlicerMeta
     #===========================================================================
diff --git a/GPy/kern/_src/linear.py b/GPy/kern/_src/linear.py
index 7d9eeac2..b6b1ec1b 100644
--- a/GPy/kern/_src/linear.py
+++ b/GPy/kern/_src/linear.py
@@ -313,3 +313,47 @@ class Linear(Kern):
 
     def input_sensitivity(self):
         return np.ones(self.input_dim) * self.variances
+
+class LinearFull(Kern):
+    def __init__(self, input_dim, rank, W=None, kappa=None, active_dims=None, name='linear_full'):
+        super(LinearFull, self).__init__(input_dim, active_dims, name)
+        if W is None:
+            W = np.ones((input_dim, rank))
+        if kappa is None:
+            kappa = np.ones(input_dim)
+        assert W.shape == (input_dim, rank)
+        assert kappa.shape == (input_dim,)
+
+        self.W = Param('W', W)
+        self.kappa = Param('kappa', kappa, Logexp())
+        self.add_parameters(self.W, self.kappa)
+
+    def K(self, X, X2=None):
+        P = np.dot(self.W, self.W.T) + np.diag(self.kappa)
+        return np.einsum('ij,jk,lk->il', X, P, X if X2 is None else X2)
+
+    def update_gradients_full(self, dL_dK, X, X2=None):
+        self.kappa.gradient = np.einsum('ij,ik,kj->j', X, dL_dK, X if X2 is None else X2)
+        self.W.gradient = np.einsum('ij,kl,ik,lm->jm', X, X if X2 is None else X2, dL_dK, self.W)
+        self.W.gradient += np.einsum('ij,kl,ik,jm->lm', X, X if X2 is None else X2, dL_dK, self.W)
+
+    def Kdiag(self, X):
+        P = np.dot(self.W, self.W.T) + np.diag(self.kappa)
+        return np.einsum('ij,jk,ik->i', X, P, X)
+
+    def update_gradients_diag(self, dL_dKdiag, X):
+        self.kappa.gradient = np.einsum('ij,i->j', np.square(X), dL_dKdiag)
+        self.W.gradient = 2.*np.einsum('ij,ik,jl,i->kl', X, X, self.W, dL_dKdiag)
+
+    def gradients_X(self, dL_dK, X, X2=None):
+        P = np.dot(self.W, self.W.T) + np.diag(self.kappa)
+        if X2 is None:
+            return 2.*np.einsum('ij,jk,kl->il', dL_dK, X, P)
+        else:
+            return np.einsum('ij,jk,kl->il', dL_dK, X2, P)
+
+    def gradients_X_diag(self, dL_dKdiag, X):
+        P = np.dot(self.W, self.W.T) + np.diag(self.kappa)
+        return 2.*np.einsum('jk,i,ij->ik', P, dL_dKdiag, X)
+
+
diff --git a/GPy/kern/_src/rbf.py b/GPy/kern/_src/rbf.py
index c2877d06..0f19dbd1 100644
--- a/GPy/kern/_src/rbf.py
+++ b/GPy/kern/_src/rbf.py
@@ -64,7 +64,7 @@ class RBF(Stationary):
             if self.ARD:
                 self.lengthscale.gradient = (dL_dpsi1[:,:,None]*_dpsi1_dlengthscale).reshape(-1,self.input_dim).sum(axis=0)
             else:
-                self.lengthscale.gradient = (dL_dpsi1[:,:,None]*_dpsi1_dlengthscale).sum()  
+                self.lengthscale.gradient = (dL_dpsi1[:,:,None]*_dpsi1_dlengthscale).sum()
 
             #from psi2
             self.variance.gradient += (dL_dpsi2 * _dpsi2_dvariance).sum()
diff --git a/GPy/testing/kernel_tests.py b/GPy/testing/kernel_tests.py
index 9ed218d8..0a74143c 100644
--- a/GPy/testing/kernel_tests.py
+++ b/GPy/testing/kernel_tests.py
@@ -276,6 +276,11 @@ class KernelGradientTestsContinuous(unittest.TestCase):
         k.randomize()
         self.assertTrue(check_kernel_gradient_functions(k, X=self.X, X2=self.X2, verbose=verbose))
 
+    def test_LinearFull(self):
+        k = GPy.kern.LinearFull(self.D, self.D-1)
+        k.randomize()
+        self.assertTrue(check_kernel_gradient_functions(k, X=self.X, X2=self.X2, verbose=verbose))
+
 #TODO: turn off grad checkingwrt X for indexed kernels like coregionalize
 # class KernelGradientTestsContinuous1D(unittest.TestCase):
 #     def setUp(self):