Lists, Vectors, Sequences
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09-13-2019, 03:33 PM
Post: #2
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RE: Lists, Vectors, Sequences
(09-12-2019 12:18 PM)Dirk.nl Wrote: Hey,A quick refresher of where vectors come from: Vectors (as in generic linear algebra terminology) are "items" in a vector space. Vector spaces can be anything: color, space, space+time, linear functions, matrices, n-tuples, and almost anything you can imagine as long as it complies with a couple of properties (which are not important right now). Now enter isomorphism: All vector spaces behave the same way and you can define 1-to-1 equivalency between items in different vector spaces. This means we can "represent" items in one vector space with items in another vector space that's easier to handle, and the easiest of all are n-tuples (bunch of numbers in a specific order). So we can for example represent the color space with n-tuples of 3 numbers (think R,G,B). Or "points" in a geometric space with 2 or 3 numerical coordinates (x,y or x,y,z). Now to your questions: * Vectors (actually the n-tuples you see on the calculator are the numeric representation of a vector) can consist of any number of values, one for each dimension of the space we are trying to represent, which is not necessarily a geometric space (the vector space being represented could be of math functions, or other weird things that have more than 3 dimensions). The difference is: a) Lists may contain things other than numbers, vectors can't (list of strings with names and phone numbers for example) b) Operations defined on lists may be different from operations defined on vectors (dot product is for vectors, concatenation or sorting of items is for lists, for example) (09-12-2019 12:18 PM)Dirk.nl Wrote: Question 2:Since a vector is a bunch of ordered numbers, doesn't really matter if it's a row or column (it's a 1D element). Only when you want to multiply a vector (1D) by a matrix (2D) you need to upconvert the vector to a 2D element, arranging the numbers in a row or column. In all other situations it doesn't matter. (09-12-2019 12:18 PM)Dirk.nl Wrote: Returning to my previous Thread “Geometry App, Distance, Intersections”. I'm not familiar with sequences, so I'll let somebody else answer this one. |
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Messages In This Thread |
Lists, Vectors, Sequences - Dirk.nl - 09-12-2019, 12:18 PM
RE: Lists, Vectors, Sequences - Claudio L. - 09-13-2019 03:33 PM
RE: Lists, Vectors, Sequences - Dirk.nl - 09-13-2019, 05:09 PM
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