Recent content by kmjonec

  1. K

    Is Matrix A Triangulable but Not Diagonalizable?

    Homework Statement Show that A = 3 4 3 -1 0 -1 1 2 3 is not diagonalizable but is triangulable and carry out triangulation (A has rational entries) I found that the only eigenvalue is 2, and that the characteristic equation is (x-2)3, but I'm...
  2. K

    Solving Nilpotent Matrices: Show det(I-A)=det(I+A)=1

    Homework Statement Show that if A is nilpotent then det(I-A)=det(I+A)=1. Homework Equations I know that det(A)=0 if A is nilpotent and det(I)=1, so this seems like it follows logically. I also know that the tr(A)=0 and that tr(I-A)=tr(I+A)=n, and that the characteristic polynomial of...