Consider a vector $a = (x,y)$.
I know that this notation $|a|$ means the magnitude of the vector which is calculated by $\sqrt{x^2 + y^2}$.
But what does this notation $\|a\|$ mean?
Thank you.
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10It often means the same thing. – Randall Feb 12 '21 at 19:39
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Did you write the same thing twice or have I missed something?? – Paul Feb 12 '21 at 19:43
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Just had a quiz where I had an equation with both of these, I don't believe they mean the same thing. – user2373804 Feb 12 '21 at 19:45
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Then ask your instructor? – Randall Feb 12 '21 at 19:45
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It's an online course unfortunately – user2373804 Feb 12 '21 at 19:46
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https://math.stackexchange.com/questions/16163/how-are-norms-different-from-absolute-values – Alessio K Feb 12 '21 at 19:54
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You have an online course with no instructor? That is disturbing. – Randall Feb 12 '21 at 19:58
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Thank you @Äres, much appreciated. – user2373804 Feb 12 '21 at 20:01
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@user2373804 You're welcome! :-) – Alessio K Feb 12 '21 at 20:02
1 Answers
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Like much of notation, it could depend on your instructor's personal style.
But, in general, the mapping $v\mapsto||v||$ refers to an arbitrary norm on the space. The go-to example for norms is magnitude or absolute value, so usually we refer to it as $|v|$. But if the problem you're talking about had a different norm function under consideration, that could explain why there was both.
Or it was a typo.