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anti-Hermitian,
skew-Hermitian, or
skew-adjoint operator or
matrixIn mathematics, a matrix is a rectangular array of numbers, symbols, or expressions. The individual items in a matrix are called its elements or entries. An example of a matrix with six elements isMatrices of the same size can be added or subtracted element by element...
is one whose adjoint is the negative of itself:
Imaginary numberAn imaginary number is any number whose square is a real number less than zero. When any real number is squared, the result is never negative, but the square of an imaginary number is always negative...
s can be thought of as skew-adjoint (since they are like 1-by-1 matrices), whereas
real numberIn mathematics, a real number is a value that represents a quantity along a continuum, such as -5 , 4/3 , 8.6 , √2 and π...
s correspond to
self-adjointIn mathematics, an element x of a star-algebra is self-adjoint if x^*=x.A collection C of elements of a star-algebra is self-adjoint if it is closed under the involution operation...
operators.