Re: [Q] symbolic SVD?

• To: mathgroup at smc.vnet.net
• Subject: [mg26838] Re: [mg26809] [Q] symbolic SVD?
• From: Daniel Lichtblau <danl at wolfram.com>
• Date: Thu, 25 Jan 2001 01:13:18 -0500 (EST)
• References: <200101240918.EAA03610@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```James wrote:
>
> Sorry about reposting.
> I've not received any reply yet,
> and I tried several ways, but I couldn't get a clue, either.
> So if anyone can help, that would be appreciated.
>
> -------------------------------------------------------------
>
> I've used 'symbolic' calculation in mathematica in many ways,
> but this time,
> I wonder if mathematica can solve symbolic matrix operation.
> Specifically,
>
>    m = {{a, b},
>         {c, d},
>         {e, f}}
>
>    SingluarValues[m]
>
> returns
>
>   SingularValues::"svdf": "SingularValues has received a matrix
>           with infinite precision."
>
> (a,b,c,d,e,f are all symbolics.)
> I need to do several symbolic matrix operations such as SingularValues.
> Is there any way to do that?
> Thank you.

Mathematica does not support SVD of symbolic (or exact numeric)
matrices. To get only the singular values you might take
Sqrt[Eigenvalues[Transpose[m].m]].

In[22]:= Sqrt[Eigenvalues[Transpose[m].m]] /.
{a->1,b->2,c->3,d->-2,e->-4,f->1} // N
Out[22]= {2.414, 5.40117}

In[23]:= SingularValues[N[m /. {a->1,b->2,c->3,d->-2,e->-4,f->1}]][[2]]
Out[23]= {5.40117, 2.414}

Finding the left and right orthogonal matrix multpliers is harder and
offhand I do not recall how one might do that.

Daniel Lichtblau
Wolfram Research

```

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