Conjugation by an invertible matrix preserves the spectrum, but does conjugation by a left/right invertible matrix also preserve spectrum? My motivating situation was considering non-unitary isometries/coisometries over an (infinite dimensional) Hilbert space. I get the feeling the answer is no, but I'm not familiar enough with Hilbert spaces to have a pet example to think about.
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Are you thinking finite matrices here? Are your left/right invertible matrices square, or can they be rectangular? – Randy E Jun 22 '15 at 13:19
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I was thinking of infinite matrices- consequently I'm not sure if square/rectangular makes sense in this context? – Jun 22 '15 at 14:08