       Re: VectorToMatrix

• To: mathgroup at smc.vnet.net
• Subject: [mg4373] Re: VectorToMatrix
• From: Paul Abbott <paul at physics.uwa.edu.au>
• Date: Mon, 15 Jul 1996 07:01:10 -0400
• Organization: University of Western Australia
• Sender: owner-wri-mathgroup at wolfram.com

```Robert Pratt wrote:

> I want to define a function VectorToMatrix[list_, n_] that behaves as
> follows:
>
> VectorToMatrix[{a,b,c,d,e,f,g,h,i,j}, 4]//MatrixForm
>
> 0 a b c d
> 0 0 e f g
> 0 0 0 h i
> 0 0 0 0 j
>
> Now n can be determined from Length[list], which will always be equal
> to n choose 2 for some n.  But I would rather input n to save that
> computation.  (I will be doing this for a lot of vectors.)

See The Mathematica Journal 4(1):34.  That example converts a vector
into a symmetric matrix.  It is easy to modify this example to meet

To convert a vector into a symmetric matrix, note that an m x m
symmetric  matrix corresponds to a vector of length m(m+1)/2 (a so-
called traingular  number). Inverting this formula:

In:= dim[n_] = (m /. Solve[m(m+1)/2 == n, m] // Last)

Out= -1 + Sqrt[1 + 8 n]
------------------
2

In:= vec = {a,b,c,d,e,f,g,h,i,j};

In:= dim[Length[vec]]

Out= 4

This is fast so you might as well compute it.

In:= VectorToMatrix[vec_ /; IntegerQ[dim[Length[vec]]]] :=
Module[{m = dim[Length[vec]],i,j},
Table[If[i>=j,0,vec[[j + (i-1)(m-i/2)-1]]],
{i, m}, {j, m+1} ]]

In:= VectorToMatrix[vec] // MatrixForm

Out//MatrixForm=
0   a   b   c   d

0   0   e   f   g

0   0   0   h   i

0   0   0   0   j

Cheers,
Paul
_________________________________________________________________
Paul Abbott
Department of Physics                       Phone: +61-9-380-2734
The University of Western Australia           Fax: +61-9-380-1014
Nedlands WA  6907                         paul at physics.uwa.edu.au
AUSTRALIA                           http://www.pd.uwa.edu.au/Paul
_________________________________________________________________

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