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peeterjoot / GAelectrodynamics

Latex sources for http://peeterjoot.com/writing/geometric-algebra-for-electrical-engineers/
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Multiplicative identity in vector space? #2

Closed sigs closed 4 years ago

sigs commented 4 years ago

Surely the multiplicative identity belongs to the field and not the vector space (since multiplication between vectors isn't yet defined).

So: https://github.com/peeterjoot/GAelectrodynamics/blob/5d779f9b855a1787e9c98659ed5cab5603afd054/prereq_vectorspace.tex#L33 Should probably be

There exists a multiplicative identity \( 1 \in \bbR \) & \( 1 \Bx = \Bx \) \\ \hline

Or simply

\( 1 \in \bbR \) is the multiplicative identity & \( 1 \Bx = \Bx \) \\ \hline

since we assume reals are already known.

peeterjoot commented 4 years ago

Fixed in e495adad263f1ddbd10089aeb4c121cb65580de8.

I've removed any mention of whether 1 is a member of the field or the vector space. This is consistent with what is done in the linear algebra books that I own.