I'm having difficulty understanding this concept of uniqueness. What's the precise definition of it? Let say we have some direct sum decomposition,(adsbygoogle = window.adsbygoogle || []).push({});

(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?

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# Uniqueness issue of direct sum decompostion of a representation?

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