1. So i have a four dimensional complex vector space ( L+ix , L+iy, L+iz, L+ig) can i choose a standard basis for it for ex: imagine that this are columns not rows ->

L+ix(1,0,0,0) + L+iy(0,1,0,0)+ L+iz(0,0,1,0)+ L+ig(0,0,0,1)=( L+ix , L+iy, L+iz, L+ig)

or they has to be a certain one?

2. Originally Posted by Sanev

L+ix(1,0,0,0) + L+iy(0,1,0,0)+ L+iz(0,0,1,0)+ L+ig(0,0,0,1)=( L+ix , L+iy, L+iz, L+ig)

or they has to be a certain one?
The RHS is a vector, not a vector basis. The LHS is not equal to the RHS, so your equality is all wrong. What you wrote above is utter nonsense.

3. Yes i'm sure it is. I'm trying to understand if i have four dimensional space how to proceed correctly. My cat vector has to be, far as a know a basis vector, and the complex coefficients witch are up front are complex vector or not?

ex. L+ix |a> ?

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