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In algebra, the reciprocal polynomial of a polynomial of degree with coefficients from an arbitrary field, such as : is the polynomial : Essentially, the coefficients are written in reverse order. They arise naturally in linear algebra as the characteristic polynomial of the inverse of a matrix. In the special case that the polynomial has complex coefficients, that is, : the conjugate reciprocal polynomial, given by, : where denotes the complex conjugate of , is also called the reciprocal polynomial when no confusion can arise. A polynomial is called self-reciprocal if . The coefficients of a self-reciprocal polynomial satisfy , and in this case is also called a palindromic polynomial. In the conjugate reciprocal case, the coefficients must be real to satisfy the condition. == Properties == Reciprocal polynomials have several connections with their original polynomials, including: # is a root of polynomial if and only if is a root of . # If then is irreducible if and only if is irreducible. # is primitive if and only if is primitive.〔 Other properties of reciprocal polynomials may be obtained, for instance: * If a polynomial is self-reciprocal and irreducible then it must have even degree.〔 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「reciprocal polynomial」の詳細全文を読む スポンサード リンク
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