       Re: Factor MatrixForm

• To: mathgroup at smc.vnet.net
• Subject: [mg21389] Re: [mg21383] Factor MatrixForm
• From: "David Park" <djmp at earthlink.net>
• Date: Sat, 1 Jan 2000 20:54:47 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Bob,

I have often wished to do the same thing because text books often have symbolic
arrays in a factored form. However, Mathematica always multiplies any factors into
a list. The only solution I know is to put the list into a HoldForm and then
remember to release it if you need to. Here are two separate routines, one for
matrices and the other for vectors which I believe will work:

factormatrix[matrix_?MatrixQ] :=
Module[{wmatrix, list, fac},
wmatrix = Map[Factor, matrix, {2}];
wmatrix = list @@ wmatrix;
fac = wmatrix /. list[{_ h_.} ..] -> h;
wmatrix = fac(#/fac & /@ wmatrix) /. list[x__] -> HoldForm[List[x]];
If[fac === 1, ReleaseHold[wmatrix], wmatrix]]

factormatrix[{{a h}, {b h}, {c h}}]
h {{a}, {b}, {c}}

factormatrix[{{a h1 h2}, {b h1 h2}, {c h1 h2}}]
h1 h2 {{a}, {b}, {c}}

factormatrix[{{a h}, {b h}, {c }}]
{{a h}, {b h}, {c}}

factormatrix[{{Cos[a]Sin[b]H}, {-Sin[a]k w H - 5Sin[b]k H}, {-2Cos[2a]H}}]
% /. HoldForm[x_] :> MatrixForm[x]
H {{Cos[a] Sin[b]}, {-k (w Sin[a] + 5 Sin[b])}, {-2 Cos[2 a]}}
- MatrixForm not shown -

factorvector[vector_?VectorQ] :=
Module[{wvector, list, fac},
wvector = Map[Factor, vector, {1}];
wvector = list @@ wvector;
fac = wvector /. list[_ h_. ..] -> h;
wvector = fac(#/fac & /@ wvector) /. list[x__] -> HoldForm[List[x]];
If[fac === 1, ReleaseHold[wvector], wvector]]

factorvector[{a h, b h, c h}]
h {a, b, c}

factorvector[{a h1 h2, b h1 h2, c h1 h2 }]
h1 h2 {a, b, c}

factorvector[{a h, b h, c }]
{a h, b h, c}

David Park

>I'm not sure what operation I want to perform on my list.  Factor
>almost does what I want.  What I have is, after many operations,
>a list in MatrixForm, something like this:
>
> MatrixForm[t]
>
> [ Cos[a]Sin[b]H - Sin[a]Sin[b]H ]
> [ -Sin[a]k*w*H - 5*Sin[b]*k*H   ]
> [   -2Cos[2a]H                  ]
>
>What manipulation do I perform to get it to look like
>
>   [ Cos[a]Sin[b] - Sin[a]Sin[b] ]
> H*[ -Sin[a]k*w - 5*Sin[b]*k     ]
>   [ -2Cos[2a]                   ]
>
>
>
>--
>----------------------------------------------------------------
> Bob Love
> rlove at neosoft.com
>----------------------------------------------------------------
>

```

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