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In mathematics, a complex square matrix is normal if : where is the conjugate transpose of . That is, a matrix is normal if it commutes with its conjugate transpose. A real square matrix satisfies , and is therefore normal if . Normality is a convenient test for diagonalizability: a matrix is normal if and only if it is unitarily similar to a diagonal matrix, and therefore any matrix satisfying the equation is diagonalizable. The concept of normal matrices can be extended to normal operators on infinite dimensional Hilbert spaces and to normal elements in C *-algebras. As in the matrix case, normality means commutativity is preserved, to the extent possible, in the noncommutative setting. This makes normal operators, and normal elements of C *-algebras, more amenable to analysis. ==Special cases== Among complex matrices, all unitary, Hermitian, and skew-Hermitian matrices are normal. Likewise, among real matrices, all orthogonal, symmetric, and skew-symmetric matrices are normal. However, it is ''not'' the case that all normal matrices are either unitary or (skew-)Hermitian. For example, : is neither unitary, Hermitian, nor skew-Hermitian, yet it is normal because : 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「normal matrix」の詳細全文を読む スポンサード リンク
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