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Non-commutative rings and algebras, non-associative algebras, universal algebra and lattice theory, linear algebra, semigroups. For questions specific to commutative algebra (that is, rings that are assumed both associative and commutative), rather use the tag ac.commutative-algebra.
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Does this formula have a rigorous meaning, or is it merely formal?
Hi Dick, I don't know if there is one or another way to give a formal meaning to this formula, but I understand it this way:
We have the identity $\det[X\ Y\ Z] = \langle X, Y \times Z\rangle$, where …