The word ``adjoint''

In mathematics the word ``adjoint'' has three meanings. One of them, the so-called Hilbert adjoint, is the one generally found in physics and engineering and it is the one used in this book. adjoint ! operator operator ! adjoint In linear algebra is a different matrix, called the adjugate matrix. It is a matrix whose elements are signed cofactors (minor determinants). For invertible matrices, this matrix is the determinant times the inverse matrix. It can be computed without ever using division, so potentially the adjugate can be useful in applications where an inverse matrix does not exist. Unfortunately, the adjugate matrix is sometimes called the adjoint matrix, particularly in the older literature. Because of the confusion of multiple meanings of the word adjoint, in the first printing of PVI, I avoided the use of the word and substituted the definition, ``conjugate transpose''. Unfortunately this was often abbreviated to ``conjugate,'' which caused even more confusion. Thus I decided to use the word adjoint and have it always mean the Hilbert adjoint found in physics and engineering.