During the recent developments of quantum theory it has been clarified thatthe observable quantities (like energy or position) may be represented byoperators (with real spectra) which are manifestly non-Hermitian. Themathematical consistency of the resulting models of stable quantum systemsrequires a reconstruction of an alternative, amended, physical inner product ofstates. We point out the less known fact that for more than one observable thetask is not always feasible. The difficulty is re-analyzed and its elementarylinear-algebraic interpretation and treatment are outlined.
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