Is anyone aware of a resource that collects examples of what complex numbers “encode” in various settings in which they naturally appear?
For example, complex numbers in the eigendecomposition of a real-valued square matrix encode permutations among dimensions in a particular eigenspace via the roots of unity — which amount to rotations. So they’re a bookkeeping device that allows the eigendecomposition of an automorphism of a real vector space to actually work in all cases.
For example, complex numbers in the eigendecomposition of a real-valued square matrix encode permutations among dimensions in a particular eigenspace via the roots of unity — which amount to rotations. So they’re a bookkeeping device that allows the eigendecomposition of an automorphism of a real vector space to actually work in all cases.