I am having difficulties with understanding some aspects of inner products. For example,(adsbygoogle = window.adsbygoogle || []).push({});

||u||² = <u,u>

Where <u,u> denoted the inner product of "u" with itself.

My problem here is that we can define any inner product we wish. For example, if I defined,

<u,v> = u1v1 + 3(u2v2)

Then the above equation for finding the magnitude of "u" doesn't agree with the other formula for finding the magnitude of the vector..

||u|| = sqrt(u1^2 + u2^2)

Why does this happen? There are other equations where this same thing happens. Shouldnt everything agree?

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# Inner product concept question.

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