The projection map onto scalar operators can be expressed in terms of the trace, concretely as:
2.
In particular they cannor be adjusted by addition of scalar operators to remove the second term on the right hand side.
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In fact, there is an internal direct sum decomposition \ mathit { gl } _ n = \ mathit { sl } _ n \ oplus k of operators / matrices into traceless operators / matrices and scalars operators / matrices.
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For example, the scalar product { \ mathbf L } \ cdot { \ mathbf S } of the two vector operators, { \ mathbf L } and { \ mathbf S }, is a scalar operator, which figures prominently in discussions of the spin-orbit interaction.
5.
For years, he had struggled to find a way to write f + g as in calculus, from the " scalar operators " in 1978, through the " til " operator in 1982, the catenation and reshape operators in 1984, the union and intersection operators in 1987, " yoke " in 1988, and finally forks in 1988.
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