Unitary transformation

Japanese: ユニタリ変換 - ユニタリへんかん（英語表記）unitary transformation

A linear transformation in an n -dimensional complex vector space Cn is expressed as an n -th order square matrix with complex numbers as components. For such a matrix A = ( a _{i j} ), the matrix with components ⁽ i.e. the complex conjugate of the transposed matrix of A ) is called the adjoint matrix of A and is represented as A ^* . The square matrix U such that U ^* U = UU ^* = 1 (identity matrix) is called a unitary matrix, and the linear transformation ^φ of Cn ^expressed as a unitary matrix is called a unitary transformation. For two vectors in Cn , is called the inner product of x and y , and is called the length of x .

Source: Heibonsha World Encyclopedia, 2nd Edition Information

Japanese:

n次元複素ベクトル空間Cⁿにおける一次変換は複素数を成分とするn次正方行列で表される。そのような行列A＝(a_ij)に対して，を成分とする行列(すなわちAの転置行列の複素共役)をAの随伴行列といい，A^*で表す。U^*U＝UU^*＝1(単位行列)なる正方行列Uをユニタリ行列といい，ユニタリ行列で表されるCⁿの一次変換φをユニタリ変換という。Cⁿの二つのベクトル，に対して，をxとyとの内積といい，また，をxの長さという。

出典　株式会社平凡社世界大百科事典第２版について　情報

<<: Unitika Co., Ltd. - Unitika

>>: Unitary representation