Unitary group

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In mathematics, the unitary group of degree n {\displaystyle n} , denoted U ⁡ ( n ) {\displaystyle \operatorname {U} (n)} , is the group of n × n {\displaystyle n\times n} unitary matrices, with the group operation of matrix multiplication. The unitary group is a subgroup of the general linear group GL ⁡ ( n , C ) {\displaystyle \operatorname {GL} (n,\mathbb {C} )} , and it has as a subgroup the special unitary group, consisting of those unitary matrices with determinant 1 {\displaystyle 1} . In the simple case n = 1 {\displaystyle n=1} , the group U ⁡ ( 1...

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