- #1
kof9595995
- 679
- 2
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?
(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?