Eigenvectors, eigenvalues of a transformation

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• Important information about eigenvectors and eigenvalues

  Therefore T is a linear transformation, because The eigenvalues and eigenvectors of T are those of A's.

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  Show that since determinant of a matrix is unchanged under unitary change of basis, argue that 1. det(A) = product of its eigenvalues for any Hermitian or Unitary A 2. use the invariance of teh trace under teh same transformation and show that Tr

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  So, if there are n distinct eigenvalues, there is a set of n linearly independent eigenvectors and this forms a basis of V.

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  For each of your eigenvectors, find the corresponding eigenvalue by inspection; then check your results by computing the eigenvalues and bases for the eigenspaces from the standard matrix for the transformation. a) Reflection about the x-axis.