Normal Matrix
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 matrix A with real entries satisfies A*=AT, and is therefore normal if ATA = AAT.
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 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.
Read more about Normal Matrix: Special Cases, Consequences, Equivalent Definitions, Analogy
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