QED Prerequisites Geometric Algebra 16: Canonical Bivectors

In this lesson we handle a few errata and then decompose a general bivector into a canonical form. Take note: we study this decomposition using a different paper, one written by Hestenes, but this is just a small diversion from our main paper.
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[@user-vl6mp8ng6l]

I am really enjoying these lectures! Thank you. I think both you (and Hestenes) jumped over something crucial in developing the canonical form around time 46:45. The argument in Hestenes was developed for even grade multivectors, but then suddenly in equation 30, the same canonical form is applied to general multivectors. I am sure it's valid, but it is not immediately obvious!

[@charlesschmidt4272]

It would be helpful to note that even multi-vectors commute with complex scalars. You assumed this property several times.

[@charlesschmidt4272]

Also, the product of a bivector and a complex scalar is a bivector.

[@PeeterJoot]

@27:31 you wrote < psi psi^~ > = alpha + I beta, but shouldn't have included that grade zero selection.

[@XylyXylyX]

Thanks again. I added an errata in the description and will address it with the next lesson.