Comment #6 on issue 1664 by ondrej.certik: Matrix([ [1, 2, 3], [4, 5, 6], [7, 8, 9] ]).eigenvects() fails http://code.google.com/p/sympy/issues/detail?id=1664
Great job! Running tests and then push in.
In [1]: M = Matrix([ [1, 2, 3], [4, 5, 6], [7, 8, 9] ])
In [2]: M.eigenvals()
Out[2]:
⎧ ⎽⎽⎽⎽ ⎽⎽⎽⎽ ⎫
⎪ 3⋅╲╱ 33 3⋅╲╱ 33 ⎪
⎨0: 1, 15/2 - ────────: 1, 15/2 + ────────: 1⎬
⎪ 2 2 ⎪
⎩ ⎭
In [3]: M.eigenvects()
Out[3]:
⎡⎛ ⎡⎡ ⎛ 12
⎞ ⎤
⎢⎜ ⎢⎢ 2⋅⎜6 +
───────────────⎟ ⎥
⎢⎜ ⎢⎢ ⎜
⎽⎽⎽⎽⎟ ⎥
⎢⎜ ⎢⎢ ⎜ 3⋅╲╱ 33
⎟ ⎥
⎢⎜ ⎽⎽⎽⎽ ⎢⎢ ⎜ 13/2 +
────────⎟ ⎥
⎢⎜ 3⋅╲╱ 33 ⎢⎢ ⎝ 2 ⎠
3 ⎥
⎢⎜15/2 + ────────, 1, ⎢⎢─────────────────────────────────── +
───────────────⎥
⎢⎜ 2 ⎢⎢⎛ ⎽⎽⎽⎽⎞ ⎛ ⎽⎽⎽⎽⎞
⎽⎽⎽⎽⎥
⎢⎜ ⎢⎢⎜ 3⋅╲╱ 33 ⎟ ⎜ 9⋅╲╱ 33 ⎟ 3⋅╲╱
33 ⎥
⎢⎜ ⎢⎢⎜13/2 + ────────⎟⋅⎜33/8 + ────────⎟ 13/2 +
────────⎥
⎢⎜ ⎢⎢⎝ 2 ⎠ ⎝ 8 ⎠
2 ⎥
⎢⎜
⎢⎢ ⎥
⎢⎜ ⎢⎢
12 ⎥
⎢⎜ ⎢⎢ 6 +
─────────────── ⎥
⎢⎜ ⎢⎢
⎽⎽⎽⎽ ⎥
⎢⎜ ⎢⎢ 3⋅╲╱
33 ⎥
⎢⎜ ⎢⎢ 13/2 +
──────── ⎥
⎢⎜ ⎢⎢
2 ⎥
⎢⎜ ⎢⎢
─────────────────── ⎥
⎢⎜ ⎢⎢
⎽⎽⎽⎽ ⎥
⎢⎜ ⎢⎢ 9⋅╲╱
33 ⎥
⎢⎜ ⎢⎢ 33/8 +
──────── ⎥
⎢⎜ ⎢⎢
8 ⎥
⎢⎜
⎢⎢ ⎥
⎣⎝ ⎣⎣
1 ⎦
⎤⎞ ⎛ ⎡⎡ ⎛ 12 ⎞
⎥⎟ ⎜ ⎢⎢ 2⋅⎜6 + ───────────────⎟
⎥⎟ ⎜ ⎢⎢ ⎜ ⎽⎽⎽⎽⎟
⎥⎟ ⎜ ⎢⎢ ⎜ 3⋅╲╱ 33 ⎟
⎥⎟ ⎜ ⎽⎽⎽⎽ ⎢⎢ ⎜ 13/2 - ────────⎟
⎥⎟ ⎜ 3⋅╲╱ 33 ⎢⎢ ⎝ 2 ⎠
⎥⎟, ⎛0, 1, ⎡⎡1 ⎤⎤⎞, ⎜15/2 - ────────, 1,
⎢⎢───────────────────────────────────
⎥⎟ ⎜ ⎢⎢ ⎥⎥⎟ ⎜ 2 ⎢⎢⎛ ⎽⎽⎽⎽⎞ ⎛
⎽⎽⎽⎽⎞
⎥⎟ ⎜ ⎢⎢-2⎥⎥⎟ ⎜ ⎢⎢⎜ 3⋅╲╱ 33 ⎟ ⎜ 9⋅╲╱
33 ⎟
⎥⎟ ⎜ ⎢⎢ ⎥⎥⎟ ⎜ ⎢⎢⎜13/2 - ────────⎟⋅⎜33/8 -
────────⎟
⎥⎟ ⎝ ⎣⎣1 ⎦⎦⎠ ⎜ ⎢⎢⎝ 2 ⎠ ⎝
8 ⎠
⎥⎟ ⎜ ⎢⎢
⎥⎟ ⎜ ⎢⎢ 12
⎥⎟ ⎜ ⎢⎢ 6 +
──────────────
⎥⎟ ⎜ ⎢⎢
⎽⎽⎽
⎥⎟ ⎜ ⎢⎢ 3⋅╲╱
33
⎥⎟ ⎜ ⎢⎢ 13/2 -
───────
⎥⎟ ⎜ ⎢⎢ 2
⎥⎟ ⎜ ⎢⎢
──────────────────
⎥⎟ ⎜ ⎢⎢
⎽⎽⎽⎽
⎥⎟ ⎜ ⎢⎢ 9⋅╲╱ 33
⎥⎟ ⎜ ⎢⎢ 33/8 -
────────
⎥⎟ ⎜ ⎢⎢ 8
⎥⎟ ⎜ ⎢⎢
⎦⎠ ⎝ ⎣⎣ 1
⎤⎤⎞⎤
⎥⎥⎟⎥
⎥⎥⎟⎥
⎥⎥⎟⎥
⎥⎥⎟⎥
3 ⎥⎥⎟⎥
+ ───────────────⎥⎥⎟⎥
⎽⎽⎽⎽⎥⎥⎟⎥
3⋅╲╱ 33 ⎥⎥⎟⎥
13/2 - ────────⎥⎥⎟⎥
2 ⎥⎥⎟⎥
⎥⎥⎟⎥
⎥⎥⎟⎥
─ ⎥⎥⎟⎥
⎽ ⎥⎥⎟⎥
⎥⎥⎟⎥
─ ⎥⎥⎟⎥
⎥⎥⎟⎥
─ ⎥⎥⎟⎥
⎥⎥⎟⎥
⎥⎥⎟⎥
⎥⎥⎟⎥
⎥⎥⎟⎥
⎥⎥⎟⎥
⎦⎦⎠⎦
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