    Basic operators and adjoints  Next: Inverse operator Up: ADJOINT DEFINED: DOT-PRODUCT TEST Previous: Automatic adjoints

## The word ``adjoint''

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.    Basic operators and adjoints  Next: Inverse operator Up: ADJOINT DEFINED: DOT-PRODUCT TEST Previous: Automatic adjoints

2014-09-27