I'm stuck already in an introductory chapter about bras and kets. I included all of the context but I'm stuck at figure 1.5.
In figure 1.5, what does $\alpha_j$ mean? In the previous figures, the subscript $i$ only held meaning as the iterated integer of the summation.
I guess I should be able to imply what it's supposed to mean based on the preceding paragraph, but I'm stuck there too.
So then how that becomes the final figure (unnumbered) is beyond me.
If someone can perceive what might be confusing me and explain in a different manner, I'd appreciate it. Thank you.