High Quality Content by WIKIPEDIA articles! In mathematics, Specht's theorem gives a necessary and sufficient condition for two matrices to be unitarily equivalent. It is named after Wilhelm Specht, who proved the theorem in 1940. Two matrices A and B are said to be unitarily equivalent if there exists a unitary matrix U such that B = U?*AU. Two matrices which are unitarily equivalent are also similar. Two similar matrices represent the same linear map, but with respect to a different basis; unitary equivalence corresponds to a change from an orthonormal basis to another orthonormal basis. If A and B are unitarily equivalent, then tr AA* = tr BB*, where tr denotes the trace (in other words, the Frobenius norm is a unitary invariant). This follows from the the cyclic invariance of the trace: if B = U ?*AU, then tr BB* = tr U?*AUU?*A*U = tr AUU?*A*UU?* = tr AA*, where the second equality is cyclic invariance.

Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.