Norms

Norms in inner product spaces. Othogonality. The Cauchy-Schwarz Inequality. The Triangle Inequality. The Parallelogram Equality.

[TheEvilKungFuMan]

*walks into bar* "Afternoon everybody"
*everyone in bar* "NORM!"

[garfieldnate]

I don't quite understand the note about when the triangle inequality yields an equality. In the proof, the inequality appears in the proof when rewriting 2 Re<u, v> as 2|<u, v>|, so shouldn't Re<u, v> = |<u, v>| be a condition for equality?

[cocacooler]

I wish you introduced norms by itselves and not necessarily induced by inner product. Because I encounter norms not induced by an inner product in my university courses and unfortunately your textbook does not prepare for that. Looks like I will need to figure out which theorems depend on writing out norm as sqrt of inner product and which don't.

[nicholaskhawlu]

Just a question if v is over R does the inner product have to map to R