Sea A matriz compleja cuadrada, entonces es una matriz normal si y sólo si donde A* es la matriz traspuesta conjugada de A (también llamado hermitiano)

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In mathematics, a complex square matrix A is normal if where A∗ is the conjugate transpose of A. That is, a matrix is normal if it commutes with its conjugate transpose. A real square matrix A satisfies A∗ = AT, and is therefore normal if ATA = AAT. 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 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.

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