Geometric Algebra for Electrical Engineers

A hardcopy of my book for myself.

January 14, 2024 Geometric Algebra for Electrical Engineers

I hadn’t printed a copy of my book for myself for about 4 years, and since I’ve added a lot since then, I wanted a new version to mark up.   This new version (V0.3.5) is now up to 313 pages, whereas my May 2019 V0.1.15-6 version weighed in at a much skinnier 258 pages.

This time, so I could see what it looked like, I got myself a hardcover copy:

The hard cover has a nice feel and thickness, and the book has a nice weight.  It also opens fairly flat, which is nice for a textbook style book.  All in all, I’m pretty impressed with the binding.  My only complaint is a small curvature to the covers.

V0.3.5 of Geometric Algebra for Electrical Engineers (and temp hardcover price drop)

December 16, 2023 Geometric Algebra for Electrical Engineers , , , , ,

Yes, I just published an update last week, but here’s another one.

Temporary price drop on hardcover.

It’s been 4 years since I printed a copy of the book for myself to mark up and edit.  In particular, having added some vector calculus identities and their geometric algebra equivalents to chapter II, it messes up the flow a bit, and I’d like a paper copy to review to help figure out how to sequence it all better.  I may just start with div and curl (in their GA forms) before moving on to curvilinear coordinates, the vector derivative and all the integration theorems, …

While I intend to mark up my copy, I’m going to treat myself to a hardcover version this time, to see what it looks like.

However, to make things a bit cheaper on myself, I’ve reduced the price on the marketplace for the hardcover version of the book to the absolute cheapest amazon will let me make it: $16.12 USD.  At that price, amazon will make some profit above printing costs, but I will not.  I believe this will also result in a price drop on the marketplace (unlike the paperback pricing, there is no explicit option to set an price for the hardcover version, so I think it’s just the USD price converted to CAD.)

So if you would like a hardcover print copy for yourself at bargain prices, now is your chance.  The paperback, in contrast, is $15.50 USD, so for only $0.62 USD more, you (and I) can get a hardcover version!  I’ll wait about a week before ordering my copy to make sure that it’s the newest version when I order, and will leave the hardcover price at $16.12 USD until I get my copy in the mail.  After that, the price will go back up, and I’ll make a couple bucks for any hardcover sales again after that.  Note that the PDF version is still available for free, as always.

If you ask “What about author proofs”.  Well, Kindle direct publishing (formerly Createspace) does have a mechanism for ordering author proofs, and if I lived in the USA, I’d use that.  However, for us poor second class Canadians, it costs just about as much to get an author proof with shipping, as just buying a copy.

What changed in this version

V0.3.5 (Dec 15, 2023)

  • Rewrite spherical polar section with the geometry first, not the coordinate representation, nor the CAS stuff.
  • Move the coordinates -> GA derivation to a problem.
  • New figure: sphericalPolarFig2.
  • update spherical polar figure1 with orientation of j.
  • Add to helpful formulas: Vector calculus identities.
  • Note about ambiguity of our curl notation.
  • Add some references to the d’Alembertian (wave equation) operator.
  • New section (chapter 2): Vector calculus identities.
  • Two (wedge) curl examples (vector field) to make things less abstract.
  • bivector field curl examples (problem.)
  • curl with polar form representation of gradient and field (problem.)
  • curl of 3D vector field example.


New version of Geometric Algebra for Electrical Engineers published.

December 9, 2023 Geometric Algebra for Electrical Engineers , , , , , ,

A new version of my book is now published.  The free PDF and the leanpub versions are available now.  The paperback and hardcover versions should be available on Amazon within the week.

What has changed:

  • V0.3.2 (Dec 8, 2023)
    • Add to helpful formulas: Determinant form of triple wedge.
    • Add figure showing the spherical polar conventions picked.
    • Add a problem showing that \( (e^x)’ = x’ e^x \) only when \( x \) and \( x’ \) commute, which is true for scalars and complex numbers, but not necessarily true for abstract entities, such as multivectors and square matrices.
    • Spherical polar coordinates: do not skip steps for \( \mathbf{x}_\phi \) computation.
    • Rewrite the Multivector potentials section. No longer pulling the ideas out of a magic hat, instead trying to motivate them.  Compromised on the strategy to do so, leaving some of the details to problems.

This potentials rewrite I’ve been working on indirectly for the last month, and have published two blog posts about the topic, as well another that I wrote and discarded, but helped me form and sequence some of the ideas.

The exponential derivative topic was also covered on my blog recently.  I’ve reworked that so that it is independent of the specific application to spherical polar coordinates, and set it as a problem for the reader (with solution at the end of chapter I in case I didn’t give enough hints in the problem statement.)

Book update. Now includes recent work on best fit solutions.

October 1, 2023 Geometric Algebra for Electrical Engineers , , , , , , , , ,


I’ve added a few new pages in the linear systems solution portion of my book, Geometric Algebra for Electrical Engineers.  This now includes the best fit content that was covered in my recent video and blog post on approximate solutions to linear systems.

The geometry that is associated with a Moore-Penrose or SVD-based pseudoinverse is not terribly obvious, and this result, providing the same answer, uses geometry exclusively.  I’ve included it in my book, since it’s a cool application, and not conceptually much trickier than the exact system solution.  This makes this section slightly more formal, as it now including an up front statement as a theorem — but that’s where formality ends, as I don’t formally prove the theorem.  I do, however, provide lots of examples and problems (with solutions), sufficient for the industrious to craft their own proof if desired.

The updated version of the book should be available on all amazon marketplaces within the next 3-5 days.  The free PDF version (and leanpub edition), both linked above, are already updated.


Updated figures in ‘Geometric Algebra for Electrical Engineers’

September 2, 2023 Geometric Algebra for Electrical Engineers , , ,

New version of the book is now published (online PDF and leanpub versions updated, with amazon updates in the approval pipeline)

  • V0.1.19-2 (Sep 2, 2023)
    • Reworked many of the Mathematica generated figures.  Now using the MaTeX[] extension to do the figure labelling (that was only done in a couple figures before this), as it looks much better, and is consistent with the fonts in the text.

      Each of these are individually very small changes, barely noticeable, but I think it makes a nice difference to overall quality.

      In many cases, I’ve generated new separate figures for the amazon paper editions of the book, using straight black instead of colors, so they don’t look as washed out, after conversion to black and white.

Here’s an example where just the captioning was changed:

The font is now whatever LaTeX uses for \\mathbf{n}, so it matches the text.

I think that the new Mathematica version (13.2) that I am using, also happens to render this 3D figure a bit nicer.

Here’s a comparison of one of the figures that now has a black and white specialization (old, new-color, new-bw):

In this particular case, I chose not to color the labels like I did previously, but I have retained that label color matching in some places.

Like I said, it’s a small difference, but the latex labelling just look better, period.  Notice that the numeric values at the tick marks on the border of the figure are not using a matching font (those are directly generated by Mathematica).  I’ll have to figure out how to make those use MaTeX too, and audit all the figures for that, but that’s a game for another day.