Matrix Representation of the Multiplicative Group of Complex Numbers
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The set of all nonzero complex numbers forms a group under complex multiplication; that is, it meets the requirement of closure, existence of identity and inverses, and associativity. There is a bijection
between
and a set of
real matrices that respects the multiplicative structure of both sets, i.e.,
, where the multiplication on the left is of nonzero complex numbers, and the multiplication on the right is of matrices. This bijection is given by
. For any complex number
,
is the matrix inverse of
.
Contributed by: Jaime Rangel-Mondragon (August 2012)
Open content licensed under CC BY-NC-SA