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

Posted 5 months ago
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 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:
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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.