diff options
Diffstat (limited to 'Linear_Algebra_by_K._Hoffman_and_R._Kunze/Chapter7.ipynb')
| -rw-r--r--[-rwxr-xr-x] | Linear_Algebra_by_K._Hoffman_and_R._Kunze/Chapter7.ipynb | 33 |
1 files changed, 19 insertions, 14 deletions
diff --git a/Linear_Algebra_by_K._Hoffman_and_R._Kunze/Chapter7.ipynb b/Linear_Algebra_by_K._Hoffman_and_R._Kunze/Chapter7.ipynb index 8aae5981..a6ddec49 100755..100644 --- a/Linear_Algebra_by_K._Hoffman_and_R._Kunze/Chapter7.ipynb +++ b/Linear_Algebra_by_K._Hoffman_and_R._Kunze/Chapter7.ipynb @@ -16,7 +16,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 3, "metadata": { "collapsed": false }, @@ -50,11 +50,11 @@ } ], "source": [ - "import numpy as np\n", - "import sympy as sp\n", - "A = sp.Matrix(([5, -6, -6],[-1, 4 ,2],[3, -6, -4]))\n", + "from numpy import array\n", + "from sympy import Symbol,Matrix\n", + "A = Matrix(([5, -6, -6],[-1, 4 ,2],[3, -6, -4]))\n", "print 'A = \\n',A\n", - "x=sp.Symbol('x')\n", + "x=Symbol('x')\n", "f = A.charpoly(x).as_expr()\n", "print 'Characteristic polynomial for linear operator T on R**3 will be:'\n", "print 'f = ',f\n", @@ -72,7 +72,7 @@ "print 'pp2 = ',p*p2\n", "print 'i.e., pp2 = f'\n", "print 'Therefore, A is similar to B'\n", - "B = np.array([[0, -2, 0],[1, 3, 0],[0, 0 ,2]])\n", + "B = array([[0, -2, 0],[1, 3, 0],[0, 0 ,2]])\n", "print 'B = \\n',B\n", "print 'Thus, we can see thet Matrix of T in ordered basis is B'" ] @@ -86,7 +86,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 4, "metadata": { "collapsed": false }, @@ -121,6 +121,9 @@ } ], "source": [ + "from numpy import array\n", + "from sympy import Symbol,Matrix\n", + "\n", "print 'A = '\n", "print '2 0 0'\n", "print 'a 2 0'\n", @@ -128,20 +131,20 @@ "a = 1#\n", "b = 0#\n", "c = 0#\n", - "A = sp.Matrix(([2, 0, 0],[a, 2, 0],[b, c, -1]))\n", + "A = Matrix(([2, 0, 0],[a, 2, 0],[b, c, -1]))\n", "print 'A = \\n',A\n", "print 'Characteristic polynomial for A is:'\n", - "x=sp.Symbol('x')\n", + "x=Symbol('x')\n", "print 'p = ',A.charpoly(x).as_expr()\n", "print 'In this case, minimal polynomial is same as characteristic polynomial.'\n", "print '-----------------------------------------'\n", "a = 0#\n", "b = 0#\n", "c = 0#\n", - "A = sp.Matrix(([2, 0, 0],[a, 2, 0],[b, c, -1]))\n", + "A = Matrix(([2, 0, 0],[a, 2, 0],[b, c, -1]))\n", "print 'A = \\n',A\n", "print 'Characteristic polynomial for A is:'\n", - "x=sp.Symbol('x')\n", + "x=Symbol('x')\n", "print 'p = ',A.charpoly(x).as_expr()\n", "print 'In this case, minimal polynomial is:',\n", "print '(x-2)(x+1)'\n", @@ -164,7 +167,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 5, "metadata": { "collapsed": false }, @@ -191,14 +194,16 @@ } ], "source": [ + "from numpy import array\n", + "from sympy import Symbol,Matrix\n", "print 'A = '\n", "print '2 0 0 0'\n", "print '1 2 0 0'\n", "print '0 0 2 0'\n", "print '0 0 a 2'\n", "print 'Considering a = 1'\n", - "A = sp.Matrix(([2, 0 ,0 ,0],[1, 2, 0, 0],[0, 0 ,2 ,0],[0, 0, 1, 2]))\n", - "x=sp.Symbol('x')\n", + "A = Matrix(([2, 0 ,0 ,0],[1, 2, 0, 0],[0, 0 ,2 ,0],[0, 0, 1, 2]))\n", + "x=Symbol('x')\n", "p = A.charpoly(x).as_expr()\n", "print 'Characteristic polynomial for A is:'\n", "print 'p = ',p\n", |