How to Transform a Matrix in Mathematica?

[guerom00]

[Mathematica] “Explose” a matrix

Hi all,

Sorry for the title
Here is what I need to do : Transform this matrix (sorry, didn't find the LaTeX for matrices; pmatrix does not work)

a b c 0 0 0 0 0 0
d e f 0 0 0 0 0 0
g h i 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0

into


a 0 0 b 0 0 c 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
d 0 0 e 0 0 f 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
g 0 0 h 0 0 i 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0

if you see what I mean… I looked into ArrayPad[] but my pattern is more complicated than a simple padding…
What's the best solution do that ?

TIA

 

[tiny-tim]

Hi guerom00!

The second matrix is the same as the top left corner of the first matrix, but with lots of zero rows and columns inserted.

So just permute the rows, and permute the columns.

 

[guerom00]

Thanks for your response

Yeah… How to permute 2 rows or 2 columns ?
Nothing more “elegant” ?

 

[guerom00]

I found this which is not bad :

 

[Gueygel]

If

A={{1,0,0},{0,0,0},{0,0,0}}
B={{a,b,c},{d,e,f},{g,h,i}}

then your first matrix is A x B and your second matrix is B x A, where "x" means tensor product. I'm not sure if new versions of Mathematica have the "tensor product" implemented, I already use an old code made by myself for that.

 

[Hepth]

I know if you have two matrices you can do:

A = {{a, b}, {c, d}}
B = {{1, 0, 0}, {0, 0, 0}, {0, 0, 0}}
Outer[Times, A, B] // ArrayFlattenI think by tensor product you mean outer product.EDIT: Changed SUM to Times (I had some for something else I was trying, TIMES is what you want.)

 

[Gueygel]

Yes, Outer[Times[]] works for tensor products of matrices.
What I use does not need ArrayFlatten...

 

[guerom00]

Thanks

Is there a general thread for random questions on Mathematica ? I don't want to open a new thread each time…
For instance, I'm looking for a pattern (to be used in a DeleteCases[]) which match a list of zeros of arbitrary length i.e. which match {0} or {0,0} or {0,0,0}, etc…
Can someone help me ?

TIA