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He does this to justify that we can define a norm over C, because the definitions speaks about vector spaces. For me that section is not necessary, because he
by youoy 2y ago
He does this to justify that we can define a norm over C, because the definitions speaks about vector spaces.
For me that section is not necessary, because he justifies the formula for the norm based on the definition of the norm, which in turn is historically justified by the norm over R2, which is by no doubt the first example of norm discovered (Pythagoras theorem).
- phkahler 2y ago>> He does this to justify that we can define a norm over C Yeah, but computing z* really involves taking apart the complex number and fiddling with the real coefficient of the imaginary part. zz* looks like an operation in C, but it's kind of not.
- tczMUFlmoNk 2y agoFor a real number `x`, does computing `-x` require "taking apart the real number and fiddling with the sign bit"? I think of negation as a real operation in R, namely a reflection about the origin, and conjugation a a real operation in C, namely a reflection about the real axis.