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Eigenvalues and operations on matrices

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The eigenvalues of a scalar multiple of a matrix are the scalar multiples of the eigenvalues.
The eigenvalues of a power of a matrix are the power the eigenvalues.
The eigenvalues of a polynomial of a matrix are the polynomial of the eigenvalues.
The eigenvalues of the inverse of a nonsingular matrix are the reciprocals of the eigenvalues.
A matrix and its transpose have the same eigenvalues/characteristic polynomial.

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Eigenvalues and operations on matrices

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