## what is the relation between vector space and the defination of vector in physics. [closed]

In physics book there are some wired definition of vector in terms of how the quantity behave under rotation of axes[Kundu P26]. Are they trying to define vector space in term of the results of special kind of map or some thing like that? or we are talking about different things? Thanks.

Kundu, Pijush K., and Ira M. Cohen. Fluid Mechanics, Second Edition. 2nd ed. Academic Press, 2001.

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 OK. I am not sure if this is off topic. I think it should be a part of Mathematical physics. I do not think i should post on physicsoverflow, physicists are less interested in those abstract math thing. – gstar2002 May 23 2012 at 17:05 See en.wikipedia.org/wiki/Pseudovector – Robert Israel May 23 2012 at 17:11 Start with a $d$-dimensional vector space $V$ (in the mathematicians' sense). A basis $\{b_1,\dots,b_d\}$ lets you represent each vector $v$ by a $d$-tuple of numbers, the coefficients in the expansion of $v$ in terms of the $b$'s. So you can think of $v$ as a function from bases of $V$ to $d$-tuples of numbers. Of course, the $d$-tuple assigned to any one basis determines the $d$-tuples assigned to all other bases, by some obvious formulas. That's the physics book's notion of vector: a function from bases to $d$-tuples of numbers, subject to suitable transformation rules. – Andreas Blass May 23 2012 at 19:05