- #1

nomadreid

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- TL;DR Summary
- Letting u,v be unit vectors, the length of the projection of u onto v is u dot v, whereas the inner product <u|v> is the projection of v onto u. Why the difference?

In simple Euclidean space: From trig, we have , for

Then I read that the inner product <

Of course one could just say that the dot product is commutative, but the reverse order of what is projecting onto what seems a bit odd.

Either: where is my mistake, or: What am I missing?

Thanks in advance.

**u**and**v**separated by angle Θ, the length of the projection of**u**onto**v**is |**u**|cosΘ; then from one definition of the dot product Θ=arcos(|**u**|⋅|**v**|/(**u**⋅**v**)); putting them together, I get the length of the projection of**u**onto**v**is**u**⋅**v**/|**v**|.Then I read that the inner product <

**u**|**v**> is the result of the projection of**v**onto**u**.Of course one could just say that the dot product is commutative, but the reverse order of what is projecting onto what seems a bit odd.

Either: where is my mistake, or: What am I missing?

Thanks in advance.