Eigenvectors/2 1 -2+i 0 i 1+i 0 0 -1+2i/Characteristic polynomial/Eigenvalues and eigenspaces/Diagonal matrix/Exercise
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We consider the linear mapping
which is given by the matrix
with respect to the standard basis.
a) Determine the characteristic polynomial and the eigenvalues of .
b) Compute, for every eigenvalue, an eigenvector.
c) Establish a matrix for with respect to a basis of eigenvectors.