Be careful using this to interpret complex eigenvalues, though! (One could argue that a complex eigenvector points along the same complex axis, but that probably doesn't help much to understand the eigenvalues of a real matrix like ( ( 0 1 ) ( 1 0 ) ).)
I didn't say that it isn't complex, only that it is real—and as such can be visualised as a transformation of the real plane, in which context one might still strive to understand its (complex) eigendecomposition.
Comments
Be careful using this to interpret complex eigenvalues, though! (One could argue that a complex eigenvector points along the same complex axis, but that probably doesn't help much to understand the eigenvalues of a real matrix like ( ( 0 1 ) ( 1 0 ) ).)
Who says ((0 1) (1 0)) is a real matrix? It's a complex matrix whose entries all happen to have 0 as the value of their imaginary part :)
I didn't say that it isn't complex, only that it is real—and as such can be visualised as a transformation of the real plane, in which context one might still strive to understand its (complex) eigendecomposition.