The textbook describes pseudovector like this:
Let a,b be vectors and c=a×b, P be the parity operator. Then P(a)=−a,P(b)=−b by definition. But P(c)=c since both a and b reverse direction. So c is a pseudovector.
I can't understand this. For I know from my math course that c is perfectly a regular vector. So P(c) should be equal to −c by definition. In the example above, however, the text seems to have assumed P(c)=P(a)×P(b), which is nonsense if c is a self-governed entity. What I can see is that c depends on a and b and any transformation on c must be computed after a and b have changed accordingly. Thus I tend to define c:=<×,(a,b)> and P(c) should actually be written as ˜P(c) where $\tilde{P}(
Am I right?
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