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Recursive parametrization and invariant phases of unitary matrices. (English) Zbl 1111.81076
Summary: We present further properties of a previously proposed recursive scheme for parametrization of $$n$$-by-$$n$$ unitary matrices. We show that the factors in the recursive formula may be introduced in any desired order. The method is used to study the invariant phases of unitary matrices. The case of four-by-four unitary matrices is investigated in detail. We also address the question of how to construct symmetric unitary matrices (i.e., unitary matrices $$U$$ that satisfy the condition $$U_{ij}=U_{ji})$$ using the recursive approach.

##### MSC:
 81R05 Finite-dimensional groups and algebras motivated by physics and their representations 15A72 Vector and tensor algebra, theory of invariants 22E70 Applications of Lie groups to the sciences; explicit representations
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##### References:
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