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Topic: VectorToMatrix
Replies: 6   Last Post: Jul 8, 1996 2:19 AM

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Paul Abbott

Posts: 1,437
Registered: 12/7/04
Re: VectorToMatrix
Posted: Jul 8, 1996 2:19 AM
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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
your needs:

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

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

In[2]:= vec = {a,b,c,d,e,f,g,h,i,j};

In[3]:= dim[Length[vec]]

Out[3]= 4

This is fast so you might as well compute it.

In[4]:= 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[5]:= VectorToMatrix[vec] // MatrixForm

0 a b c d

0 0 e f g

0 0 0 h i

0 0 0 0 j

Paul Abbott
Department of Physics Phone: +61-9-380-2734
The University of Western Australia Fax: +61-9-380-1014
Nedlands WA 6907

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