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SKEW SYMMETRY OF A CLASS OF OPERATORS. Li, Chun Guang; Zhou, Ting Ting. Banach Journal of Mathematical Analysis; Durham Vol. 8, Iss. 1, (2014): 279-294. As we know, unitary transformations in Hilbert space are the operations executed by a quantum computation. The physical system that may serve as a platform for As we are all aware by now that equal matrices have equal dimensions, hence only the square matrices can be symmetric or skew-symmetric form. Let S be a maximal skew - symmetric implementation of 8 . The class of J - symmetric representations of the * -algebra D ( 8 ) J - equivalent to ng isAn operator T on a complex Hilbert space H is said to be skew symmetric if there exists a conjugate-linear, isometric involution C : H ! H such that CTC Every real n-by-n matrix B is skew symmetric if and only if Dot[B.x, The next lemma shows that, for a sufficiently large class of operators,

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