If two matrices A and B commute, when is it true that rho(A+B) = rho(A)+rho(B), i.e. that the spectral radius of A+B is equal to the sum of the two spectral radii or A and B?
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What if $\displaystyle B=-A$?
Thanks, with B = -A I guess it holds trivially, is there any other set of conditions that ensures this?
Why does it hold? The spectral radius of the zero matrix is zero; so if your formula held, every matrix would have a zero spectral radius.
shoot! of course but is it true at least that if A and B commute then rho(A+B)<=rho(A)+rho(B)? I think yes. My question is really, when does this hold with equality.
Originally Posted by chrysi shoot! of course but is it true at least that if A and B commute then rho(A+B)<=rho(A)+rho(B)? I think yes. My question is really, when does this hold with equality. Sorry for reading your question too fast. It might be true!
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