       Re: Can't quite figure out tensors

• To: mathgroup at smc.vnet.net
• Subject: [mg96985] Re: Can't quite figure out tensors
• From: "Sjoerd C. de Vries" <sjoerd.c.devries at gmail.com>
• Date: Sun, 1 Mar 2009 04:55:15 -0500 (EST)
• References: <go8in6\$lg2\$1@smc.vnet.net>

```The tensor product of two matrices m1 and m2 is given by Outer
[Times,m1,m2] if that's your question. Depending on your needs, you
may throw in an ArrayFlatten

Cheers -- Sjoerd

On Feb 27, 1:27 pm, Aaron Fude <aaronf... at gmail.com> wrote:
> Hi,
>
> I'm trying to write code that will produce Christoffel symbols for
> various coordinate systems. I would like to use the definition that
> yields Gamma_ij^k as the partial of the covariant basis e_i with
> respect to variables x^j dotted with the contravariant vector e^k. So
> far I have
>
> z[r_, theta_] := {r Cos[theta], r Sin[theta]}
> ei[r_, theta_] := {Derivative[1, 0][z][r, theta],
>   Derivative[0, 1][z][r, theta]}
> gij[r_, theta_] := ei[r, theta].Transpose[ei[r, theta]]
> gIJ[r_, theta_] := Inverse[gij[r, theta]]
> deidxj[r_, theta_] := {Derivative[1, 0][zi][r, theta],
>   Derivative[0, 1][zi][r, theta]}
>
> and now i need to form the tensor product
> deidxj * gIJ * ei
>
> and it has proven to be a bit to intense for me to pull off. Could
> someone show me how to do that?
>
> Many thanks in advance,
>
> Aaron

```

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