Geometric Algebra for Electrical Engineers

New version of Geometric Algebra for Electrical Engineers published.

December 9, 2023 Geometric Algebra for Electrical Engineers No comments , , , , , ,

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.


Hardcover physics class notes.

March 13, 2021 math and physics play , , , , , , , , , , , , , ,

Amazon’s kindle direct publishing invited me to their hardcover trial program, and I’ve now made hardcover versions available of most of my interesting physics notes compilations:

Instead of making hardover versions of my classical mechanics, antenna theory, and electromagnetic theory notes, I have unpublished the paperback versions. These are low quality notes, and I don’t want more people to waste money on them (some have.) The free PDFs of all those notes are still available.

My geometric algebra book is also available in both paperback and hardcover (black and white). I’ve unpublished the color version, as it has a much higher print cost, and I thought it was too confusing to have all the permutations of black-and-white/color and paperback/hardcover.

Hardcover edition of Geometric Algebra for Electrical Engineers.

February 27, 2021 Uncategorized , , , ,

I was invited to Kindle Direct Publishing‘s hardcover beta program, and have made my geometric algebra book available in black and white hardcover.

As always, the PDF, leanpub edition, and latex sources are also available.

I thought that it was too confusing to have color and black-and-white editions of the book (color has a significantly higher printing cost), so I have unpublished the color editions of the book (softcover, and hardcover). There is one copy of the color edition left, and once that is sold, it will show as out of print.

Some nice positive feedback for my book.

October 31, 2020 math and physics play , , , , , , , , , ,

Here’s a fun congratulatory email that I received today for my Geometric Algebra for Electrical Engineers book

Peeter ..
I had to email to congratulate you on your geometric algebra book. Like yourself, when I came across it, I was totally blown away and your book, being written from the position of a discoverer rather than an expert, answers most of the questions I was confronted by when reading Doran and Lasenby’s book.
You’re a C++ programmer and from my perspective, when using natural world math, you are constructing a representation of a problem (like code does) except many physicists do not recognize this. They’re doing physics with COBOL (or C with classes!).
.. Reader
I couldn’t resist pointing out the irony of his COBOL comment, as my work at LzLabs is now heavily focused on COBOL (and PL/I) compilers and compiler runtimes.  You could say that my work, at work or at play, is all an attempt to transition people away from the evils of legacy COBOL.
For reference the Doran and Lasenby book is phenomenal work, but it is really hard material.  To attempt to read this, you’ll need a thorough understanding of electromagnetism, relativity, tensor algebra, quantum mechanics, advanced classical mechanics, and field theory.  I’m still working on this book, and it’s probably been 12 years since I bought it.  I managed to teach myself some of this material as I went, but also took most of the 4th year UofT undergrad physics courses (and some grad courses) to fill in some of the gaps.
When I titled my book, I included “for Electrical Engineers” in the title.  That titling choice was somewhat derivative, as there were already geometric algebra books “for physicists”,  and “for computer science“.  However, I thought it was also good shorthand for the prerequisites required for the book as “for Electrical Engineers” seemed to be good shorthand for “for a student that has seen electromagnetism in its div, grad, curl form, and doesn’t know special relativity, field theory, differential forms, tensor algebra, or other topics from more advanced physics.”
The relativistic presentation of electromagnetism in Doran and Lasenby, using the Dirac algebra (aka Space Time Algebra (STA)), is much more beautiful than the form that I have used in my book.  However, I was hoping to present the subject in a way that was accessible, and provided a stepping stone for the STA approach when the reader was ready to tackle a next interval of the “learning curve.”