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2017-12-26 14:43:36 -0500 received badge  Student (source)
2017-12-19 06:51:53 -0500 commented answer Matrix Permutations

Thanks for your help. @vdelecroix I'll try to comprehend your solution ...

2017-12-19 06:49:14 -0500 received badge  Scholar (source)
2017-12-16 15:19:56 -0500 commented answer Matrix Permutations

I think, now I get your point:

The 1st step remains and the I'll do this:

CountOfInvertibleMatrices3Tuples = len(invertibleMatrices)^3

Is it now ok?


2017-12-16 14:55:27 -0500 commented answer Matrix Permutations

I don't think that I do so.

I perform the following steps:

  1. I put all invertible Matrices in the variable invertibleMatrices.
  2. I try to build all tuple-combinations with 3 matrices and put it in the variable invertibleMatrices3Tuples.
  3. I build the products of matrices in each tuple and see if the product is invertible and put them all in the variable invertibleSTUProducts.

Did I miss something?

2017-12-16 13:55:31 -0500 commented answer Matrix Permutations

Thanks for your help.

I tried it as follow based on your code, but it doesn't work. I use CoCalc. It shows the green bar for computation, but it doesn't stop and doesn't return any results.

R = [0,1,2,3,4,5,6,7,8,9]

C = cartesian_product((R,R,R,R)).list()

invertibleMatrices = [matrix(ZZ, 2,2,list(c)) for c in C if matrix(ZZ, 2,2,list(c)).det()]

invertibleMatrices3Tuples = cartesian_product((invertibleMatrices, invertibleMatrices, invertibleMatrices)).list()

invertibleSTUProducts = [c for c in invertibleMatrices3Tuples if c[0]*c[1]*c[2].det()]

BTW: What do you mean by "It is a good idea to use structure in mathematics"?

2017-12-15 22:47:56 -0500 asked a question Matrix Permutations


how do I get all permutations of a Matrix?

For the following exercise I would like to get all permutations of a Matrix with integer values in the range $0$ to $9$. There should be $10^4$ permutations. And then generate the permutations of tuples with three matrices. $10^{12}$ permutations and then I would filter the list somehow for the invertible matrices.

Is there a better way?

Exercise: Let $S, T, U \in \mathbb{R}^{2x2}$ such that, $S_{i, j}, T_{i, j}, U_{i, j} \in {0,1, \cdots, 9}$ How many of the products $S \cdot T \cdot U$ are invertible?

In the Sage reference for permutation I couldn't find any thing.


PS: The curly braces couldn't be escaped properly in the LaTex part ... \{0,1, \cdots, 9\}