Details and Options
- A matrix m is normal if m.ConjugateTranspose[m]ConjugateTranspose[m].m.
- NormalMatrixQ works for symbolic as well as numerical matrices.
- The following options can be given:
SameTest Automatic function to test equality of expressions Tolerance Automatic tolerance for approximate numbers
- For exact and symbolic matrices, the option SameTest->f indicates that two entries aij and bij are taken to be equal if f[aij,bij] gives True where a=m.m and b=m.m.
- For approximate matrices, the option Tolerance->t can be used to indicate that the norm γ=m.m-m.m∞ satisfying γ≤t γ∞ is taken to be zero where γ∞ is the infinity norm of the matrix m.
Examplesopen allclose all
An approximate MachinePrecision matrix:
Properties & Relations (9)
NormalMatrixQ[m] is effectively equivalent to m.mm.m:
A normal matrix is always diagonalizable as tested with DiagonalizableMatrixQ:
Introduced in 2014