Conveying inner product with words

[qubyte]

I was wondering about the proper way to say, $\langle$A$|$B$\rangle$ .

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, $\frac{x^{2} + 2d}{5}$ , is "x squared plus two d all over five."
How would you do the same with $\langle$A$|$B$\rangle$ ?

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.

 

[TheOldHag]

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.

 

[qubyte]

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?

 

[AlephZero]

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.

 

[blue_raver22]

The proper way to say \langleA|B\rangle is "the inner product of A with B." This follows the standard mathematical notation, where the first term in the inner product, A, is placed before the second term, B, and the angle brackets are read as "inner product." So, in your example, the expression would be conveyed as "the inner product of x squared plus two d all over five."

As for literature where this is exemplified, any introductory linear algebra textbook or course material should provide examples and explanations of inner products and their notation. You can also refer to mathematical resources online, such as Khan Academy or MIT OpenCourseWare, for further clarification.