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Uniqueness issue of direct sum decompostion of a representation?

  1. Sep 20, 2011 #1
    I'm having difficulty understanding this concept of uniqueness. What's the precise definition of it? Let say we have some direct sum decomposition,
    (1)Are [itex]\left( {\begin{array}{*{20}{c}}
    {{R_1}} & 0 \\
    0 & {{R_2}} \\
    \end{array}} \right)[/itex] and [itex]\left( {\begin{array}{*{20}{c}}
    {{R_2}} & 0 \\
    0 & {{R_1}} \\
    \end{array}} \right)[/itex]the same decomposition?
    (2)Are [itex]\left( {\begin{array}{*{20}{c}}
    {{R_1}} & 0 \\
    0 & {{R_2}} \\
    \end{array}} \right)[/itex] and[itex]\left( {\begin{array}{*{20}{c}}
    {{R_1}} & 0 \\
    0 & {{U^{ - 1}}{R_2}U} \\
    \end{array}} \right)[/itex]the same decomposition?
     
  2. jcsd
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