**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**=*A*T, and is therefore normal if *A*T*A* = *AA*T.

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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“As all historians know, the past is a great darkness, and filled with echoes. Voices may reach us from it; but what they say to us is imbued with the obscurity of the *matrix* out of which they come; and try as we may, we cannot always decipher them precisely in the clearer light of our day.”

—Margaret Atwood (b. 1939)

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—Gilbert Keith Chesterton (1874–1936)