Others, such as matrix addition, scalar multiplication, matrix multiplication, and row operations involve operations on matrix entries and therefore require that matrix entries are numbers or belong to a field or a ring. To find the adjoint of a matrix, you simply have to swap elements a11 with a22 and switch the signs of elements a12 and a21 from positive to negative or vice. ![]() Some, such as transposition and submatrix do not depend on the nature of the entries. 22), is most commonly denoted using dagger notation A (Arfken 1985). ![]() The analogous concept applied to an operator instead of a matrix, sometimes also known as the Hermitian conjugate (Griffiths 1987, p. ![]() In linear algebra, it refers to the conjugate transpose and is most commonly denoted A(H). There are a number of basic operations that can be applied on matrices. The word adjoint has a number of related meanings.
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