I have to figure out why in case of square matrix $A$ $\sigma(A) = σ(A_1)$, where $A_1 = GAG^T$ and $G$ is a Givens matrix. Any tips and help would be very appreciated since I spent a lot of time on research without any answer.
The spectrum of symmetric givens operation on square non zero matrix.
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matrices
measure-theory
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0What is a Givens matrix? – 2017-01-03
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0It is a matrix which will compute a particular Givens rotation on a matrix. – 2017-01-03
1 Answers
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$G$ is real orthogonal. Hence $GAG^T=GAG^{-1}$ is similar to $A$ and they have identical spectra.
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0Thank you, your answer is perfect. – 2017-01-03