diff --git a/ext/cvmat.cpp b/ext/cvmat.cpp
index 130e9ad..eb1f398 100644
--- a/ext/cvmat.cpp
+++ b/ext/cvmat.cpp
@@ -1159,6 +1159,7 @@ rb_aref(VALUE self, VALUE args)
   default:
     scalar = cvGetND(CVARR(self), index);
   }
+
   return cCvScalar::new_object(scalar);
 }
 
@@ -1568,7 +1569,7 @@ rb_rand_shuffle_bang(int argc, VALUE *argv, VALUE self)
  * call-seq:
  *   lut(<i>lookup_table</i>) -> cvmat
  *
- * Return new matrix performed lookup-table transforme.
+ * Return new matrix performed lookup-table transform.
  *
  * <i>lookup_table</i> should be CvMat that have 256 element (e.g. 1x256 matrix).
  * Otherwise, raise CvStatusBadArgument error.
@@ -2122,7 +2123,10 @@ rb_transform(int argc, VALUE *argv, VALUE self)
   VALUE transmat, shiftvec;
   rb_scan_args(argc, argv, "11", &transmat, &shiftvec);
   VALUE dest = new_object(cvGetSize(CVARR(self)), cvGetElemType(CVARR(self)));
-  cvTransform(CVARR(self), CVARR(dest), CVMAT(transmat), MASK(shiftvec));
+  if (NIL_P(shiftvec))
+    cvTransform(CVARR(self), CVARR(dest), CVMAT(transmat), NULL);
+  else
+    cvTransform(CVARR(self), CVARR(dest), CVMAT(transmat), CVMAT(shiftvec));
   return dest;
 }
 
diff --git a/test/test_cvmat.rb b/test/test_cvmat.rb
index 5843993..46f6de7 100755
--- a/test/test_cvmat.rb
+++ b/test/test_cvmat.rb
@@ -1552,6 +1552,71 @@ class TestCvMat < OpenCVTestCase
     assert_equal(2, max_loc.y)
     assert_equal(3, max_loc.x)
   end
+
+  def test_dot_product
+    m1 = create_cvmat(2, 2, :cv32f, 1) { |j, i, c|
+      CvScalar.new(c * 0.5)
+    }
+    m2 = create_cvmat(2, 2, :cv32f, 1) { |j, i, c|
+      CvScalar.new(c * 1.5)
+    }
+    assert_in_delta(10.5, m1.dot_product(m2), 0.001)
+
+    m1 = create_cvmat(2, 2, :cv32f) { |j, i, c|
+      CvScalar.new(c * 0.5, c * 0.6, c * 0.7, c * 0.8)
+    }
+    m2 = create_cvmat(2, 2, :cv32f) { |j, i, c|
+      CvScalar.new(c * 1.5, c * 2.0, c * 2.5, c * 3.0)
+    }
+    assert_in_delta(85.39999, m1.dot_product(m2), 0.001)
+  end
+
+  def test_cross_product
+    m1 = create_cvmat(1, 3, :cv32f, 1) { |j, i, c|
+      CvScalar.new(c * 0.5)
+    }
+    m2 = create_cvmat(1, 3, :cv32f, 1) { |j, i, c|
+      CvScalar.new(c + 1)
+    }
+    m3 = m1.cross_product(m2)
+
+    assert_in_delta(CvScalar.new(-0.5), m3[0, 0], 0.001)
+    assert_in_delta(CvScalar.new(1), m3[0, 1], 0.001)
+    assert_in_delta(CvScalar.new(-0.5), m3[0, 2], 0.001)
+  end
+
+  def test_transform
+    m0 = create_cvmat(5, 5, :cv32f, 3) { |j, i, c|
+      CvScalar.new(c * 0.5, c * 1.0, c * 1.5)
+    }
+    transmat = CvMat.new(3, 3, :cv32f, 1);
+    transmat[0, 0] = CvScalar.new(0.0)
+    transmat[1, 0] = CvScalar.new(0.0)
+    transmat[2, 0] = CvScalar.new(0.0)
+
+    transmat[0, 1] = CvScalar.new(0.0)
+    transmat[1, 1] = CvScalar.new(0.0)
+    transmat[2, 1] = CvScalar.new(1.0)
+
+    transmat[0, 2] = CvScalar.new(1.0)
+    transmat[1, 2] = CvScalar.new(0.0)
+    transmat[2, 2] = CvScalar.new(0.0)
+
+    m1 = m0.transform(transmat)
+    assert_each_cvscalar(m1, 0.01) { |j, i, c|
+      CvScalar.new(c * 1.5, 0, c, 0)
+    }
+
+    stf = CvMat.new(3, 1, :cv32f, 1)
+    stf[0, 0] = CvScalar.new(-10)
+    stf[1, 0] = CvScalar.new(0.0)
+    stf[2, 0] = CvScalar.new(5)
+
+    m1 = m0.transform(transmat, stf)
+    assert_each_cvscalar(m1, 0.01) { |j, i, c|
+      CvScalar.new(c * 1.5 - 10, 0, c + 5, 0)
+    }
+  end
 end