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I'm confused by what you mean when you say renaming the vectors should have no effect... Why would you ever rename them, and how can you write an equation <u, v> = <v, u> when in reality you are just saying <u, v> = <u, v>?


I think he means that it is fine to assign them different names. It doesn't matter whether you call the top vector u or v, as long as you know it is the top vector. (So <u,v> and <v,u> are actually referring to two different images)


What could be an inner product function for comparing images, like in the last slide?