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Matrices as operators

  • To: mathgroup at
  • Subject: [mg122993] Matrices as operators
  • From: Chris Young <cy56 at>
  • Date: Sun, 20 Nov 2011 05:34:20 -0500 (EST)
  • Delivered-to:

I'd like to be able to abbreviate matrices such as rotation matrices so 
that I don't have to repeat the argument. This way I can pass in more 
complicated arguments and it also shows the structure of the 
transformation more clearly.

Through[( {
    {Cos, -Sin},
    {Sin, Cos}
   } )[θ]]

will get me partway there:

Out: {{Cos, -Sin}[θ], {Sin, Cos}[θ]}

I have to apply Thread and Through again to finally get what I want:

In: Thread[Through[{{Cos, -Sin}[θ], {Sin, Cos}[θ]}]]

Out: {{Cos[θ], (-Sin)[θ]}, {Sin[θ], Cos[θ]}}

Is there a shortcut way to do this all in one step?

Thanks very much for any help.

Chris Young
cy56 at

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