Adjoint

The term "adjoint" has several different meanings, depending on the context in which it is used:

In linear algebra, the adjoint of a matrix is the transpose of its cofactor matrix. It is sometimes also called the adjugate.

In functional analysis, the adjoint of a linear operator between two Hilbert spaces is a related linear operator that maps the second Hilbert space into the dual space of the first. It is denoted by a superscript asterisk, and is sometimes called the Hermitian adjoint or conjugate transpose.

In differential equations, the adjoint equation is a related equation to the original equation that is obtained by taking the complex conjugate of the equation and reversing the direction of the differential operators.

In optimization theory, the adjoint method is a technique for computing gradients of a function that involves solving a related set of equations, known as the adjoint equations.

Overall, the term "adjoint" refers to a related concept or object that is derived from or associated with another concept or object.