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Math Help - Diagonal matrix

  1. #1
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    Diagonal matrix

    Suppose that a 2x2 real matrix has the form . For which values of the numbers a and b will B be diagonalizable by a real matrix? Explain.
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  2. #2
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    Remember that when you diagonalize a matrix B, the diagonal values of the resulting diagonalized matrix will be the eigenvalues of B, and that a matrix P such that P^{-1}BP is diagonal will have as it's columns the eigenvectors corresponding to those eigenvalues. Thus, we require that B have real eigenvectors. As our matrix is real, real eigenvalues are a necessary condition for real eigenvectors.
    Note that \det(I\lambda-B)=0 gives (\lambda-a)^2+b^2=0.
    This should point you in the right direction.

    --Kevin C.
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