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Thread: eigenvalues

  1. #1
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    eigenvalues

    if A is a singular matrix, must 0 be an eigenvalue of A?

    my logic relied on the fact that the determinant of a singular matrix = 0... is this correct?
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  2. #2
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    Quote Originally Posted by ktcyper03 View Post
    if A is a singular matrix, must 0 be an eigenvalue of A?

    my logic relied on the fact that the determinant of a singular matrix = 0... is this correct?

    Yes to your question, though your logic works if you know that the determinant of a square matrix is \pm the free coefficient if the matrix's characteristic polynomial...

    Tonio
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  3. #3
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    Quote Originally Posted by tonio View Post
    Yes to your question, though your logic works if you know that the determinant of a square matrix is \pm the free coefficient if the matrix's characteristic polynomial...

    Tonio
    Or if you know that the determinant of any matrix is just the product of all of its eigenvalues.
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