 Solution

ID: past-exam-of-the-numerical-analysis-course-of-the-university-of-oxford/2014/3/c/solution

The determinant is invariant under transpose. Therefore the characteristic polynomials coincide:

det (λ I - A^{T}) = det ((λ I - A)^{T}) = det (λ I - A) .

Their polynomial roots, including their algebraic multiplicities, are the same, so

A

and

A^{T}

have the same eigenvalues. This allows column sums as well as row sums to supply Gershgorin discs for the same spectrum.

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