Freeman Posted August 27, 2005 Share Posted August 27, 2005 Can a vector be a wave? Or does the wave need to be a number of vectors? Link to comment Share on other sites More sharing options...
matt grime Posted August 27, 2005 Share Posted August 27, 2005 eh? offer a mathematical defintion of wave and one of a vector and see. don't confuse mathematics with physics, or a model of something with the thing itself either. Link to comment Share on other sites More sharing options...
ElijahJones Posted August 27, 2005 Share Posted August 27, 2005 There is no mathematical definition of a wave. Waves are physical phenomena. There are functions that gets used to model waves, sine and cosine functions, functions of complex variables, fourier series etc. A vector V in its most general form is simply an ordered n-tuple whose elements are taken from a space S. Since vector operations are usually only meaningful when constructed from the operations of S, we choose S to be a set with some operations that give algebraic structure usually a field. An n-dimensional vector space can be contructed from the set of n-tuples taken over a field F by defining vector addition in natural ways from the operations of F. You must also include F as the set of scalar multipliers satisfying certain conditions. On top of this is usually defined an inner product (the dot product on multivariate calculus). If you want a really hard but excellent text try Dummit and Foote "Absract Algebra". I have 2nd edition but it may be into a third or fourth by now. Link to comment Share on other sites More sharing options...
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