Message Boards Message Boards

GROUPS:

Represent and compute with matrix-valued functions of a vector?

Posted 5 months ago
850 Views
|
2 Replies
|
1 Total Likes
|

In the attachment I pose a problem of representing and computing with a matrix-valued function of a vector. Before I go to the effort of learning Mathematica, I would like to know that it can do these kinds of computations and yield results in the usual notation or something close to it. I would appreciate any guidance, including being told that my request is impossible. Thanks.

Attachments:
2 Replies
Posted 5 months ago

To Gianluca: Thank you for the Mathematica code. I will definitely find a way to try this.

It can be done:

m[\[Sigma]_] := With[{coeff = 1/Sqrt[1 - \[Sigma].\[Sigma]]},
   ArrayFlatten[{{coeff, {coeff*\[Sigma]}},
     {coeff*Transpose[{\[Sigma]}],
      IdentityMatrix[Length[\[Sigma]]] +
       (coeff - 1) 1/\[Sigma].\[Sigma]*
        KroneckerProduct[\[Sigma], \[Sigma]]}}]];
m[{a, b, c}]

You have to get used to an unusual way of thinking about row and column vectors.

Reply to this discussion
Community posts can be styled and formatted using the Markdown syntax.
Reply Preview
Attachments
Remove
or Discard

Group Abstract Group Abstract