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==Definition==
Let ''H'' be a Hilbert space. A bounded operator ''A'' on ''H'' is said to be '''subnormal''' if ''A'' has a normal [[Extension (mathematics)|extension]]{{dn|date=April 2012}}. In other words, ''A'' is subnormal if there exists a Hilbert space ''K'' such that ''H'' can be embedded in ''K'' and there exists a normal operator ''N'' of the form
:<math>N = \begin{bmatrix} A & B\\ 0 & C\end{bmatrix}</math>
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