Uniqueness issue of direct sum decompostion of a representation?

[kof9595995]

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 $\left( {\begin{array}{*{20}{c}}<br /> {{R_1}} & 0 \\<br /> 0 & {{R_2}} \\<br /> \end{array}} \right)$ and $\left( {\begin{array}{*{20}{c}}<br /> {{R_2}} & 0 \\ <br /> 0 & {{R_1}} \\<br /> \end{array}} \right)$the same decomposition?
(2)Are $\left( {\begin{array}{*{20}{c}}<br /> {{R_1}} & 0 \\<br /> 0 & {{R_2}} \\<br /> \end{array}} \right)$ and$\left( {\begin{array}{*{20}{c}}<br /> {{R_1}} & 0 \\<br /> 0 & {{U^{ - 1}}{R_2}U} \\<br /> \end{array}} \right)$the same decomposition?

 

[fresh_42]

Not the same, but isomorphic.