Frobenius Norm

Author

Eric W. Weisstein
May 2, 2007

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

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

©2007 Wolfram Research, Inc. except for portions noted otherwise

Check

Equal@@With[{m=Array[a,{3,2}]},
{
Sqrt[Tr[m.Transpose[Conjugate[m]]]]//FullSimplify,
Norm[m,Frobenius],
Sqrt[Plus@@(Abs[Flatten[m]]^2)]
}
]

Equal@@With[{m=Array[a,{3,3}]},
{
Sqrt[Tr[m.Transpose[Conjugate[m]]]]//FullSimplify,
Norm[m,Frobenius],
Sqrt[Plus@@(Abs[Flatten[m]]^2)]
}
]

Equal@@With[{m=Array[a,{4,4}]},
{
Sqrt[Tr[m.Transpose[Conjugate[m]]]]//FullSimplify,
Norm[m,Frobenius],
Sqrt[Plus@@(Abs[Flatten[m]]^2)]
}
]