Conveying inner product with words

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Discussion Overview

The discussion revolves around the proper verbal expression of the inner product notation \langleA|B\rangle, particularly focusing on the order of A and B in the phrasing. Participants explore the implications of this order in different contexts, such as complex versus real vector spaces, and seek clarity on how to convey this mathematical concept verbally.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant suggests saying "the inner product of A with B," questioning the correct order of A and B in the expression.
  • Another participant states that the inner product of A and B should be expressed with A in the first slot, particularly in complex vector spaces, while noting that the order does not matter for real vector spaces.
  • A participant reiterates the importance of the order in complex vector spaces and requests examples to clarify this point.
  • Another participant argues that the phrase "the inner product of A and B" is not ambiguous, comparing it to the expression "A minus B," which is generally understood to mean A minus B rather than B minus A.

Areas of Agreement / Disagreement

Participants express differing views on the ambiguity of the phrase "the inner product of A and B," with some asserting that the order is critical in certain contexts while others believe it is clear enough as stated. The discussion remains unresolved regarding the best way to convey the inner product verbally.

Contextual Notes

Participants highlight the potential for ambiguity in environments where left-to-right reading is not the norm, suggesting that context may influence how the inner product should be expressed.

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I was wondering about the proper way to say, [itex]\langle[/itex]A[itex]|[/itex]B[itex]\rangle[/itex] .

I have recently heard, "The inner product of A with B." But I'm not sure if this is correct. Does anyone know the proper order in which to place A and B in the sentence?

As a simple example: Suppose you're speaking with someone on the phone. Then one way to convey the expression, [itex]\frac{x^{2} + 2d}{5}[/itex] , is "x squared plus two d all over five."
How would you do the same with [itex]\langle[/itex]A[itex]|[/itex]B[itex]\rangle[/itex] ?

If someone could also point me in the direction of some literature where this is exemplified, that would very kind.
I must have missed this some where along the line, and I can't seem to find a solid answer anywhere.
 
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The inner product of A and B with A in the first slot. This order qualifier is necessary in the case of a complex vector space. For reals the order doesn't matter.
 
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TheOldHag said:
The inner product of A and B with A in the first slot. This order qualifier is necessary in the case of a complex vector space. For reals the order doesn't matter.

I appreciate the response. Anywhere I may be able to find an explicit example of this?
 
Since western languages are read and written from left to right, I don't think "the inner product of A and B" is any more ambiguous than "A minus B," which nobody would interpret as meaning ##B-A##.

Of course if you are in an environment where left-to-right writing is not a universal rule, you might need to be more careful.
 

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