vector space

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[knotty sandal]

im not really sure which of the axioms dont hold when the field is C

[obsidian hornet]

hint: Consider iSK_2, the set of SK_2 matrices scaled by i

[knotty sandal]

i dont rly understand the sk_2 thing very well

[obsidian hornet]

SK_2 is the set of skew-hermition 2x2 matrices

[knotty sandal]

i was just trying to see if i could make the axioms not work based on any matrix over complex field i wasnt rly considering the sk2 part

[obsidian hornet]

I mean, you're showing SK_2 isnt a C-vector space

so if SK_2 never came up, you didnt read the question

[knotty sandal]

im thinking about a 2x2 sk2 matrix right now

and the only general 'rule' i guess i can see that makes the matrix sk2 is that the real part of 12 entry is equal to -1 * real part of 21 entry

so im wondering if i can kind of use that as part of my answer?

[obsidian hornet]

Hint: refer back to the hint I gave

part of being a vector space is the operations are well defined

per the hint, I'm suggestion scalar multiplication on SK_2 is illdefined when the scalar field is C.

[knotty sandal]

so if you multiply by i then the matrix is no longer skew hermitian?

[obsidian hornet]

that's the hint, yes.

since, if $A$ is skew-hermitian, then $(iA)^\ast=i^\ast A^\ast=(-i)(-A)=iA$

[fierce surge]

Omegabet_

[obsidian hornet]

so iA is Hermitian

[knotty sandal]

hmmm ok thx

+close