Example of diagonalisable matrix with given property












0














Let $Ain M_5(mathbb C)$ satisfying $(A^2-I)^2=0$ and $A$ is not diagonal matrix.



Then I have To find matrix A



But I tried but adding some terms in up to diagonal Nilpotency occur Which prevent form diagonalisable.



Please Help me to find example






linear-algebra examples-counterexamples diagonalization







share|cite|improve this question



























    0














    Let $Ain M_5(mathbb C)$ satisfying $(A^2-I)^2=0$ and $A$ is not diagonal matrix.



    Then I have To find matrix A



    But I tried but adding some terms in up to diagonal Nilpotency occur Which prevent form diagonalisable.



    Please Help me to find example






    linear-algebra examples-counterexamples diagonalization







    share|cite|improve this question

























      0












      0








      0







      Let $Ain M_5(mathbb C)$ satisfying $(A^2-I)^2=0$ and $A$ is not diagonal matrix.



      Then I have To find matrix A



      But I tried but adding some terms in up to diagonal Nilpotency occur Which prevent form diagonalisable.



      Please Help me to find example






      linear-algebra examples-counterexamples diagonalization







      share|cite|improve this question













      Let $Ain M_5(mathbb C)$ satisfying $(A^2-I)^2=0$ and $A$ is not diagonal matrix.



      Then I have To find matrix A



      But I tried but adding some terms in up to diagonal Nilpotency occur Which prevent form diagonalisable.



      Please Help me to find example






      linear-algebra examples-counterexamples diagonalization




      linear-algebra examples-counterexamples diagonalization






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked yesterday









      MathLover

      46210




      46210






















          2 Answers
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          0














          The following Jordan matrix has minimal polynomial $p(lambda)=(lambda-1)^2(lambda+1)^2=(lambda^2-1)^2$:
          $$
          A= left[begin{array}{cccc}
          -1 & 1 & 0 & 0 & 0\
          0 & -1 & 0 & 0 & 0\
          0 & 0 & 1 & 1 & 0\
          0 & 0 & 0 & 1 & 0\
          0 & 0 & 0 & 0 & 1end{array}right]
          $$






          share|cite|improve this answer





















          • Sir but above matrix is not diagonalisable. I wanted Diagonalisable
            – MathLover
            5 hours ago



















          0














          Write $(A-Id)^2(A+Id)^2$ instead of $(A^2-I)^2$. Consider for instance the $(4, 4)$ matrix with diagonal entries $1,1,-1,-1, 1$, the ligne just over the diagonal $1,0,1,0$ and ll other coefficients $0$.



          You can also find diagonalisable matrix : any symmetry does the job.






          share|cite|improve this answer























          • Sir I want matrix other than diagonal matrix.I had mentioned that in question
            – MathLover
            11 hours ago










          • But the line over the digaonal is (1,0,1,0) , please draw the matrix..
            – Thomas
            7 hours ago










          • I tried but That is not diagonalisable
            – MathLover
            5 hours ago











          Your Answer





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          2 Answers
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          2 Answers
          2






          active

          oldest

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          active

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          0














          The following Jordan matrix has minimal polynomial $p(lambda)=(lambda-1)^2(lambda+1)^2=(lambda^2-1)^2$:
          $$
          A= left[begin{array}{cccc}
          -1 & 1 & 0 & 0 & 0\
          0 & -1 & 0 & 0 & 0\
          0 & 0 & 1 & 1 & 0\
          0 & 0 & 0 & 1 & 0\
          0 & 0 & 0 & 0 & 1end{array}right]
          $$






          share|cite|improve this answer





















          • Sir but above matrix is not diagonalisable. I wanted Diagonalisable
            – MathLover
            5 hours ago
















          0














          The following Jordan matrix has minimal polynomial $p(lambda)=(lambda-1)^2(lambda+1)^2=(lambda^2-1)^2$:
          $$
          A= left[begin{array}{cccc}
          -1 & 1 & 0 & 0 & 0\
          0 & -1 & 0 & 0 & 0\
          0 & 0 & 1 & 1 & 0\
          0 & 0 & 0 & 1 & 0\
          0 & 0 & 0 & 0 & 1end{array}right]
          $$






          share|cite|improve this answer





















          • Sir but above matrix is not diagonalisable. I wanted Diagonalisable
            – MathLover
            5 hours ago














          0












          0








          0






          The following Jordan matrix has minimal polynomial $p(lambda)=(lambda-1)^2(lambda+1)^2=(lambda^2-1)^2$:
          $$
          A= left[begin{array}{cccc}
          -1 & 1 & 0 & 0 & 0\
          0 & -1 & 0 & 0 & 0\
          0 & 0 & 1 & 1 & 0\
          0 & 0 & 0 & 1 & 0\
          0 & 0 & 0 & 0 & 1end{array}right]
          $$






          share|cite|improve this answer












          The following Jordan matrix has minimal polynomial $p(lambda)=(lambda-1)^2(lambda+1)^2=(lambda^2-1)^2$:
          $$
          A= left[begin{array}{cccc}
          -1 & 1 & 0 & 0 & 0\
          0 & -1 & 0 & 0 & 0\
          0 & 0 & 1 & 1 & 0\
          0 & 0 & 0 & 1 & 0\
          0 & 0 & 0 & 0 & 1end{array}right]
          $$







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered 8 hours ago









          DisintegratingByParts

          58.7k42579




          58.7k42579












          • Sir but above matrix is not diagonalisable. I wanted Diagonalisable
            – MathLover
            5 hours ago


















          • Sir but above matrix is not diagonalisable. I wanted Diagonalisable
            – MathLover
            5 hours ago
















          Sir but above matrix is not diagonalisable. I wanted Diagonalisable
          – MathLover
          5 hours ago




          Sir but above matrix is not diagonalisable. I wanted Diagonalisable
          – MathLover
          5 hours ago











          0














          Write $(A-Id)^2(A+Id)^2$ instead of $(A^2-I)^2$. Consider for instance the $(4, 4)$ matrix with diagonal entries $1,1,-1,-1, 1$, the ligne just over the diagonal $1,0,1,0$ and ll other coefficients $0$.



          You can also find diagonalisable matrix : any symmetry does the job.






          share|cite|improve this answer























          • Sir I want matrix other than diagonal matrix.I had mentioned that in question
            – MathLover
            11 hours ago










          • But the line over the digaonal is (1,0,1,0) , please draw the matrix..
            – Thomas
            7 hours ago










          • I tried but That is not diagonalisable
            – MathLover
            5 hours ago
















          0














          Write $(A-Id)^2(A+Id)^2$ instead of $(A^2-I)^2$. Consider for instance the $(4, 4)$ matrix with diagonal entries $1,1,-1,-1, 1$, the ligne just over the diagonal $1,0,1,0$ and ll other coefficients $0$.



          You can also find diagonalisable matrix : any symmetry does the job.






          share|cite|improve this answer























          • Sir I want matrix other than diagonal matrix.I had mentioned that in question
            – MathLover
            11 hours ago










          • But the line over the digaonal is (1,0,1,0) , please draw the matrix..
            – Thomas
            7 hours ago










          • I tried but That is not diagonalisable
            – MathLover
            5 hours ago














          0












          0








          0






          Write $(A-Id)^2(A+Id)^2$ instead of $(A^2-I)^2$. Consider for instance the $(4, 4)$ matrix with diagonal entries $1,1,-1,-1, 1$, the ligne just over the diagonal $1,0,1,0$ and ll other coefficients $0$.



          You can also find diagonalisable matrix : any symmetry does the job.






          share|cite|improve this answer














          Write $(A-Id)^2(A+Id)^2$ instead of $(A^2-I)^2$. Consider for instance the $(4, 4)$ matrix with diagonal entries $1,1,-1,-1, 1$, the ligne just over the diagonal $1,0,1,0$ and ll other coefficients $0$.



          You can also find diagonalisable matrix : any symmetry does the job.







          share|cite|improve this answer














          share|cite|improve this answer



          share|cite|improve this answer








          edited 7 hours ago

























          answered 23 hours ago









          Thomas

          3,864510




          3,864510












          • Sir I want matrix other than diagonal matrix.I had mentioned that in question
            – MathLover
            11 hours ago










          • But the line over the digaonal is (1,0,1,0) , please draw the matrix..
            – Thomas
            7 hours ago










          • I tried but That is not diagonalisable
            – MathLover
            5 hours ago


















          • Sir I want matrix other than diagonal matrix.I had mentioned that in question
            – MathLover
            11 hours ago










          • But the line over the digaonal is (1,0,1,0) , please draw the matrix..
            – Thomas
            7 hours ago










          • I tried but That is not diagonalisable
            – MathLover
            5 hours ago
















          Sir I want matrix other than diagonal matrix.I had mentioned that in question
          – MathLover
          11 hours ago




          Sir I want matrix other than diagonal matrix.I had mentioned that in question
          – MathLover
          11 hours ago












          But the line over the digaonal is (1,0,1,0) , please draw the matrix..
          – Thomas
          7 hours ago




          But the line over the digaonal is (1,0,1,0) , please draw the matrix..
          – Thomas
          7 hours ago












          I tried but That is not diagonalisable
          – MathLover
          5 hours ago




          I tried but That is not diagonalisable
          – MathLover
          5 hours ago


















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