Status: NeedsDecision
Owner: [email protected]
Labels: Type-Enhancement Priority-Medium Matrices Polynomial
New issue 2268 by [email protected]: Sorting of eigenvalues in resulted
diagonal form of matrix.
http://code.google.com/p/sympy/issues/detail?id=2268
It will be better, that they were returned in order (and so they would also
be put in order in the D matrix).
For example:
In [1]: a = Matrix([[3, -1, 0], [-1, 2, -1], [0, -1, 3]])
In [2]: a.diagonalize()
Out[2]:
⎛⎡1 0 0⎤, ⎡1 1 -1⎤⎞
⎜⎢ ⎥ ⎢ ⎥⎟
⎜⎢0 4 0⎥ ⎢2 -1 0 ⎥⎟
⎜⎢ ⎥ ⎢ ⎥⎟
⎝⎣0 0 3⎦ ⎣1 1 1 ⎦⎠
At least for real numbers it is cleare.
But also it is connected with the Jordan blocks ordering.
"In mathematics there are no standards about order of jordan blocks (even
that one's can be placed below diagonal). But in our lecture it is
convenient this standard of order:
- in decreasing order of image part of eigenvalues
- in decreasing order of real part of eigenvalues
- in decreasing order of sizes of jordan cells
We can use this or similar standard (or increasing instead of decreasing)
in sympy to obtain required order (1, 3, 4). Saying as parameter of methods
(standard_order=True).
I supposed that the similar standard for findings root of polynomials can
be used too. (eigenvalues are obtained with the help of this procedure), or
by options what sort of ording is needed.
So I set NeedsDecision how exactly, please express your opinion.
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