Normal Matrix

Author

Eric W. Weisstein
January 10, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/LinearAlgebra/NormalMatrix.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/NormalMatrix.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Example

{NormalMatrixQ[m={{I,0},{0,3-5I}}],HermitianQ[m]}

m.Transpose[m]

Transpose[m].m

Enumeration

(-1,0,1)-Matrices

Table[Count[Matrices[n,{-1,0,1}],_?NormalMatrixQ],{n,3}]//Timing

(-1,1)-Matrices

Table[Count[Matrices[n,{-1,1}],_?NormalMatrixQ],{n,4}]//Timing

(0,1)-Matrices

Table[Count[Matrices[n],_?NormalMatrixQ],{n,4}]//Timing

All normal matrices are diagonalizable

Table[And@@DiagonalizableQ/@Select[Matrices[n],NormalMatrixQ],{n,4}]//Timing