Note that there are several notations in common use for the complex conjugate. Applied physics and engineering texts tend to prefer , while most modern math and theoretical physics texts favor
. Unfortunately, the notation is also commonly used to denote adjoint
operators matrices. Because of these mutually contradictory conventions, care is
needed when consulting the literature. In this work, is used to denote the complex conjugate.

Common notational conventions for complex conjugate are summarized in the table below.

notation

references

This work; Abramowitz and Stegun (1972,
p. 16), Anton (2000, p. 528), Harris and Stocker (1998, p. 21), Golub
and Van Loan (1996, p. 15), Kaplan (1981, p. 28), Kaplan (1992, p. 572),
Krantz (1999, p. 2), Kreyszig (1988, p. 568), Roman (1987, p. 534),
Strang (1988, p. 220), Strang (1993)

Arfken (1985,
p. 356), Bekefi and Barrett (1987, p. 616), Press et al. (1989, p. 397),
Harris and Stocker (1998, p. 21), Hecht (1998, p. 18), Herkommer (1999,
p. 262)

In linear algebra, it is common to apply both the complex conjugate and transpose to the same matrix. The matrix obtained from a given matrix by this combined operation is commonly called the conjugate
transpose
of .
However, the terms adjoint matrix, adjugate matrix, Hermitian conjugate, and Hermitian
adjoint are also used, as are the notations and . In this work, is used to denote the conjugate
transpose matrix and is used to denote the adjoint
operator.