Canonical

Appendix A

Sometimes the word canonical is misused to mean natural, obvious or dictated by circumstances.

We jokingly say that if a=3 than a+5 is canonically equal to 8.

We could talk about canonical forms and mention that \dfrac{3}{6} and \dfrac{1}{2} are equal but that \dfrac{1}{2} is preferred–it is the canonical form.

Appendix B

A Canonical basis is a set of vectors where the components of each vector are all 0 except for a single entry that is one.

Example:

  • {1,0,0,0}
  • {0,1,0,0}
  • {0,0,1,0}
  • {0,0,0,1}

Appendix C

One mention hinted that if something was canonical then it would not depend on the basis set. Search efforts have not yet found any corroboration. So far it it seems that canonical means the best of all acceptable choices.