diff --git a/lib/matplotlib/transforms.py b/lib/matplotlib/transforms.py
index 8a5ac9e33114..4752ff6e255b 100644
--- a/lib/matplotlib/transforms.py
+++ b/lib/matplotlib/transforms.py
@@ -2094,11 +2094,18 @@ def skew(self, xShear, yShear):
         calls to :meth:`rotate`, :meth:`rotate_deg`, :meth:`translate`
         and :meth:`scale`.
         """
-        rotX = math.tan(xShear)
-        rotY = math.tan(yShear)
-        skew_mtx = np.array(
-            [[1.0, rotX, 0.0], [rotY, 1.0, 0.0], [0.0, 0.0, 1.0]], float)
-        self._mtx = np.dot(skew_mtx, self._mtx)
+        rx = math.tan(xShear)
+        ry = math.tan(yShear)
+        mtx = self._mtx
+        # Operating and assigning one scalar at a time is much faster.
+        (xx, xy, x0), (yx, yy, y0), _ = mtx.tolist()
+        # mtx = [[1 rx 0], [ry 1 0], [0 0 1]] * mtx
+        mtx[0, 0] += rx * yx
+        mtx[0, 1] += rx * yy
+        mtx[0, 2] += rx * y0
+        mtx[1, 0] += ry * xx
+        mtx[1, 1] += ry * xy
+        mtx[1, 2] += ry * x0
         self.invalidate()
         return self