|
In mathematics, an involutory matrix is a matrix that is its own inverse. That is, multiplication by matrix A is an involution if and only if A2 = I. Involutory matrices are all square roots of the identity matrix. This is simply a consequence of the fact that any nonsingular matrix multiplied by its inverse is the identity.〔.〕 ==Examples== The 2 × 2 real matrix is involutory provided that 〔Peter Lancaster & Miron Tismenetsky (1985) ''The Theory of Matrices'', 2nd edition, pp 12,13 Academic Press ISBN 0-12-435560-9〕 One of the three classes of elementary matrix is involutory, namely the ''row-interchange elementary matrix''. A special case of another class of elementary matrix, that which represents multiplication of a row or column by −1, is also involutory; it is in fact a trivial example of a signature matrix, all of which are involutory. Some simple examples of involutory matrices are shown below. : where :I is the identity matrix (which is trivially involutory); :R is an identity matrix with a pair of interchanged rows; :S is a signature matrix. Clearly, any block-diagonal matrices constructed from involutory matrices will also be involutory, as a consequence of the linear independence of the blocks. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「involutory matrix」の詳細全文を読む スポンサード リンク
|