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I started learning quantum, and I got a bit confused about inner and dot products.

I've attached 2 screenshots; 1 from Wikipedia and 1 from an MIT pdf I found online.

Wikipedia says that a.Dot(b) when they're complex would be the sum of a

The PDF from MIT (https://ocw.mit.edu/courses/physics...all-2013/lecture-notes/MIT8_05F13_Chap_04.pdf) page 2 says that the inner product is taken <a|b>, then when doing a1b1+a2b3+... the complex conjugate of a is taken. I thought this would be the same thing as taking the dot product with complex numbers (like what I mentioned above in the 2nd paragraph). But in the dot product, the complex conjugate of b is taken, whereas here the complex conjugate of a is taken.

Could someone demystify this for me please?

Thanks

I've attached 2 screenshots; 1 from Wikipedia and 1 from an MIT pdf I found online.

Wikipedia says that a.Dot(b) when they're complex would be the sum of a

_{i}b_{i}where b is the complex conjugate.The PDF from MIT (https://ocw.mit.edu/courses/physics...all-2013/lecture-notes/MIT8_05F13_Chap_04.pdf) page 2 says that the inner product is taken <a|b>, then when doing a1b1+a2b3+... the complex conjugate of a is taken. I thought this would be the same thing as taking the dot product with complex numbers (like what I mentioned above in the 2nd paragraph). But in the dot product, the complex conjugate of b is taken, whereas here the complex conjugate of a is taken.

Could someone demystify this for me please?

Thanks