1 files changed, 13 insertions, 13 deletions
diff --git a/Linear_Algebra_by_K._Hoffman_and_R._Kunze/Chapter10.ipynb b/Linear_Algebra_by_K._Hoffman_and_R._Kunze/Chapter10.ipynb
index 1c137a08..24d02247 100755..100644
--- a/Linear_Algebra_by_K._Hoffman_and_R._Kunze/Chapter10.ipynb
+++ b/Linear_Algebra_by_K._Hoffman_and_R._Kunze/Chapter10.ipynb
@@ -46,7 +46,7 @@
     }
    ],
    "source": [
-    "import numpy as np\n",
+    "from numpy import array,transpose\n",
     "print 'a = [x1 x2]'\n",
     "print 'b = [y1 y2]'\n",
     "print 'f(a,b) = x1*y1 + x1*y2 + x2*y1 + x2*y2'\n",
@@ -54,12 +54,12 @@
     "print '[x1  x2]  *  |1   1|  *   |y1|'\n",
     "print '              |1   1|     |y2|'\n",
     "print 'So the matrix of f in standard order basis B = {e1,e2} is:'\n",
-    "fb = np.array([[1, 1],[1, 1]])\n",
+    "fb = array([[1, 1],[1, 1]])\n",
     "print '[f]B = \\n',fb\n",
-    "P = np.array([[1 ,1],[-1, 1]])\n",
+    "P = array([[1 ,1],[-1, 1]])\n",
     "print 'P = \\n',P\n",
     "print 'Thus, [f]B'' = P''*[f]B*P'\n",
-    "fb1 = np.transpose(P) * fb * P\n",
+    "fb1 = transpose(P) * fb * P\n",
     "print '[f]B'' = \\n',fb1"
    ]
   },
@@ -81,23 +81,23 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "n =  56.0\n",
-      "a =  410.0\n",
-      "b =  70.0\n",
-      "f(a,b) =  28700.0\n",
+      "n =  24.0\n",
+      "a =  100.0\n",
+      "b =  40.0\n",
+      "f(a,b) =  4000.0\n",
       "f is non-degenerate billinear form on R**n.\n"
      ]
     }
    ],
    "source": [
-    "import numpy as np\n",
-    "n = round(np.random.randint(2,90))\n",
-    "a = round(np.random.randint(1,n) * 10)#\n",
-    "b = round(np.random.randint(1,n) * 10)#\n",
+    "from numpy import random,transpose\n",
+    "n = round(random.randint(2,90))\n",
+    "a = round(random.randint(1,n) * 10)#\n",
+    "b = round(random.randint(1,n) * 10)#\n",
     "print 'n = ',n\n",
     "print 'a = ',a\n",
     "print 'b = ',b\n",
-    "f = a * np.transpose(b)\n",
+    "f = a * transpose(b)\n",
     "print 'f(a,b) = ',f\n",
     "print 'f is non-degenerate billinear form on R**n.'\n",
     "#end"