answers: orthogonal
context: can also be generalised to a wider sort of inverses, e.g. matrix inverses. Every number excluding zero has a reciprocal, and reciprocals of certain irrational numbers can have important special properties. Examples include the reciprocal of e (≈ 0.367879) and the golden ratio's reciprocal (≈ 0.618034). The first reciprocal is special because no other positive number can produce a lower number when put to the power of itself; formula_17 is the global minimum of formula_18. The second number is the only positive number that is equal to its reciprocal plus one:formula_19. Its additive inverse is the only negative number that </s> its conjugate transpose); that is, A is Hermitian if A square complex matrix whose transpose is equal to the negation of its complex conjugate is called a skew-Hermitian matrix; that is, A is skew-Hermitian if A square matrix whose transpose is equal to its inverse is called an orthogonal matrix; that is, A is orthogonal if A square complex matrix whose transpose is equal to its conjugate inverse is called a unitary matrix; that is, A is unitary if If A is an "m" × "n" matrix and A is its transpose, then the result of matrix multiplication with these </s> entries, then where denotes the entry-wise complex conjugate of a matrix. This results of applying to the definition of matrix product the fact that the conjugate of a sum is the sum of the conjugates of the summands and the conjugate of a product is the product of the conjugates of the factors. Transposition acts on the indices of the entries, while conjugation acts independently on the entries themselves. It results that, if and have complex entries, one has where denotes the conjugate transpose (conjugate of the transpose, or equivalently transpose of the conjugate). Given three matrices and , the
question: when does the transpose of a matrix equal the inverse