. . . . "1073950518"^^ . . . . . . . . . . . . . . . . . . . . . . . . . "In mathematics, a complex square matrix A is normal if it commutes with its conjugate transpose A*: The concept of normal matrices can be extended to normal operators on infinite dimensional normed 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."@en . . "170366"^^ . "In mathematics, a complex square matrix A is normal if it commutes with its conjugate transpose A*: The concept of normal matrices can be extended to normal operators on infinite dimensional normed 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. The spectral theorem states that a matrix is normal if and only if it is unitarily similar to a diagonal matrix, and therefore any matrix A satisfying the equation A*A = AA* is diagonalizable. The converse does not hold because diagonalizable matrices may have non-orthogonal eigenspaces. The left and right singular vectors in the singular value decomposition of a normal matrix differ only in complex phase from each other and from the corresponding eigenvectors, since the phase must be factored out of the eigenvalues to form singular values."@en . . . . . . . . . . . "12483"^^ . . . . . "Normal matrix"@en . . . . . . . . . . . .