InterviewSolution
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InterviewSolution
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Show that if `lambda_(1), lambda_(2), ...., lamnda_(n)` are `n` eigenvalues of a square matrix a of order n, then the eigenvalues of the matric `A^(2)` are `lambda_(1)^(2), lambda_(2)^(2),..., lambda_(n)^(2)`. |
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Answer» `AX=lambdaX` or `A(AX)=A(lambdaX)` or `A^(2)X=lambda(AX)=lambda(lambdaX)=lambda^(2)X` i.e., `A^(2)X=lambda^(2)X` Hence, eigenvalue of `A^(2)` is `lambda^(2)`. Thus, if `lambda_(1), lambda_(2), ..., lambda_(n)` are eigenvalue of A, then `lambda_(1)^(2), lambda_(2)^(2), ..., lambda_(n)^(2)` are eigenvalues of `A^(2)`. |
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