Uniqueness issue of direct sum decompostion of a representation?

kof9595995
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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 \left( {\begin{array}{*{20}{c}}<br /> {{R_1}} &amp; 0 \\<br /> 0 &amp; {{R_2}} \\<br /> \end{array}} \right) and \left( {\begin{array}{*{20}{c}}<br /> {{R_2}} &amp; 0 \\ <br /> 0 &amp; {{R_1}} \\<br /> \end{array}} \right)the same decomposition?
(2)Are \left( {\begin{array}{*{20}{c}}<br /> {{R_1}} &amp; 0 \\<br /> 0 &amp; {{R_2}} \\<br /> \end{array}} \right) and\left( {\begin{array}{*{20}{c}}<br /> {{R_1}} &amp; 0 \\<br /> 0 &amp; {{U^{ - 1}}{R_2}U} \\<br /> \end{array}} \right)the same decomposition?
 
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Not the same, but isomorphic.
 

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