Diagonal matrices

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Let $D_n$ be the set of all n*n complex diagonal matrices. Does there exist a unitary matrix $U$ in $M_n(mathbbC)$ but not in $D_n$ such that $UD_nU^*= D_n$?




linear-algebra matrices linear-transformations




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    Let $D_n$ be the set of all n*n complex diagonal matrices. Does there exist a unitary matrix $U$ in $M_n(mathbbC)$ but not in $D_n$ such that $UD_nU^*= D_n$?




    linear-algebra matrices linear-transformations




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      Let $D_n$ be the set of all n*n complex diagonal matrices. Does there exist a unitary matrix $U$ in $M_n(mathbbC)$ but not in $D_n$ such that $UD_nU^*= D_n$?




      linear-algebra matrices linear-transformations




      share|cite|improve this question











      Let $D_n$ be the set of all n*n complex diagonal matrices. Does there exist a unitary matrix $U$ in $M_n(mathbbC)$ but not in $D_n$ such that $UD_nU^*= D_n$?





      linear-algebra matrices linear-transformations





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      asked Jul 28 at 17:23









      rkmath

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          Any permutation matrix will work. For instance
          $$U=pmatrix0&1&0&cdots&0\
          1&0&0&cdots&0\0&0&1&cdots&0\
          vdots&vdots&vdots&ddots&vdots\
          0&0&0&cdots&1.$$






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            1 Answer
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            active

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            up vote
            4
            down vote



            accepted










            Any permutation matrix will work. For instance
            $$U=pmatrix0&1&0&cdots&0\
            1&0&0&cdots&0\0&0&1&cdots&0\
            vdots&vdots&vdots&ddots&vdots\
            0&0&0&cdots&1.$$






            share|cite|improve this answer

























              up vote
              4
              down vote



              accepted










              Any permutation matrix will work. For instance
              $$U=pmatrix0&1&0&cdots&0\
              1&0&0&cdots&0\0&0&1&cdots&0\
              vdots&vdots&vdots&ddots&vdots\
              0&0&0&cdots&1.$$






              share|cite|improve this answer























                up vote
                4
                down vote



                accepted







                up vote
                4
                down vote



                accepted






                Any permutation matrix will work. For instance
                $$U=pmatrix0&1&0&cdots&0\
                1&0&0&cdots&0\0&0&1&cdots&0\
                vdots&vdots&vdots&ddots&vdots\
                0&0&0&cdots&1.$$






                share|cite|improve this answer













                Any permutation matrix will work. For instance
                $$U=pmatrix0&1&0&cdots&0\
                1&0&0&cdots&0\0&0&1&cdots&0\
                vdots&vdots&vdots&ddots&vdots\
                0&0&0&cdots&1.$$







                share|cite|improve this answer













                share|cite|improve this answer



                share|cite|improve this answer











                answered Jul 28 at 17:39









                Lord Shark the Unknown

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