In "Quantum Computation and Quantum Information" by Nielsen & Chuang, on pp. 88-89, applying basic statistical definitions to operators, one of the intermediary steps uses the expression(adsbygoogle = window.adsbygoogle || []).push({});

M-<M>

where M is a Hermitian operator, and <M> is the expected value = <ψ|M|ψ> for a given vector ψ (that is, when one is testing for |ψ>.)

What I do not understand is how one can subtract a vector from an operator. That is, <ψ|M|ψ> is a vector, and M is an operator. For example, if one took an example of M as a 2x2 matrix and ψ as a 1x2 vector, then <ψ|M|ψ> is a 1x2 vector, and then M-<M> has a mismatch in dimensions.

What am I wrongly interpreting? Thanks.

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# M-<M> for M operator: why not a mismatch?

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