In mathematics, the word ``adjoint'' has two meanings.
One, the so-called Hilbert adjoint,
is generally found in physics and engineering
and it is the one used in this book.
In linear algebra there is a different matrix,
called the adjugate matrix.
It is a matrix with elements that
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
in which 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, ``conjugate transpose'' 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.