Dot Product Calculator Quandry

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Discussion Overview

The discussion revolves around the calculation of the dot product for two complex vectors, A and B. Participants explore the correct method for computing the dot product, particularly in the context of complex numbers and their implications in quantum mechanics.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant expresses confusion over differing results from a calculator and manual calculation of the dot product, suggesting a potential misunderstanding in the calculation method.
  • Another participant questions the use of parentheses, implying that notation may affect the calculation.
  • A participant resolves their confusion by stating that the conjugate of the second vector must be taken in the calculation, indicating a specific requirement for complex inner products.
  • A later reply confirms the necessity of taking the conjugate of the second vector for the inner product, explaining that this ensures the result is a real number when a vector is dotted with itself.

Areas of Agreement / Disagreement

While one participant resolves their confusion regarding the conjugate, there is no explicit consensus on the initial calculation method or the implications of the results, leaving some uncertainty in the discussion.

Contextual Notes

The discussion highlights the importance of understanding complex vector operations, particularly in relation to quantum mechanics, but does not delve into the specifics of the mathematical steps or definitions that may be relevant.

infraray
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I'm going nuts here and I can't figure this out. I have two complex vectors:
A=(1+i)x + (1)y +(i)z
B=(4-i)x +(0)y + (2-2i)z
If I do the dot product of these on my calculator I get 1 + 7i, however when I do this by hand I keep getting 7 +5i. What am I doing wrong? When figuring this out by hand I am going by the assumption that AB=AxBx + AyBy + AzBz.
 
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Are you using parentheses properly?
 
I figured it out. I need to take the conjugate of the second vector. This is sure going to get confusing with Quantum Mechanics!
 
infraray said:
I figured it out. I need to take the conjugate of the second vector.

Yes that's correct, for a complex inner product you take the conjugate of the second argument. It's defined that way so that if you take the inner product of a vector with itself then you'll always end up with just a real number. This real number is called the "norm" and is a generalized measure of the length of the vector.
 
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