Question of the day

 

Let  be given by  for a fixed Let  be a linear transformation such that  is a set of linearly independent eigenvectors of  Then

  1. The matrix of  with respect to  is diagonal.
  2. The matrix of  with respect to  isnon-diagonal.
  3. The matrix of  with respect to  is not necessarily diagonal, but is upper triangular.
  4. The matrix of  with respect to  is diagonal, but the matrix of  with respect to  is not diagonal.

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