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Are 'lists' and vectors the same thing? 
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#1
Feb1213, 08:11 AM

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I've just been reading through the first few pages of 'Linear Algebra Done Right' by S. Axler and so far, the concept of a 'list' seems a lot like a vector. Are they one and the same?
If so, is there a reason why Axler chose to call it a list? Perhaps maybe to rid the idea that a vector is a 'directed line segment'? Thanks 


#2
Feb1213, 09:06 AM

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PF Gold
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I don't have that book so cannot see exactly how he defines "list" but, at least according to any definition I would consider reasonable, no, they are not the same. I would take a "list" to be an ordered sequence. I can, have, for example, my grocery list: bread, milk, tuna fish, green beans, potatoes. That is pretty much equivalent to the "list" data type you will find in Pascal, C++ or Java.
Now, while there are many different, more or less equivalent, ways to define "vector", they all give an algebraic structure. We must be able to add two vectors and multiply a vector by a number (or, more generally, an element of a field). That is certainly NOT the case for the "list" above. If he is saying "a list of numbers with defined addition and scalar multiplication", that would be the same but I can see no good reason for the nonstandard terminology. 


#3
Feb1213, 09:13 AM

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#4
Feb1213, 09:51 AM

P: 194

Are 'lists' and vectors the same thing?
(Thank goodness for "Look Inside" on Amazon! ) 


#5
Feb1213, 11:06 PM

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PF Gold
P: 3,289

As I recall, he uses lists to group objects much as you would do with a set, but with two differences: first, the order in which the elements appear is significant, so (1,2) is not the same as (2,1); and second, there can be repetitions, so you can have a list like (2,2) which is distinct from (2), something you can't do with sets.



#6
Feb1313, 07:39 AM

P: 333

Makes sense now, thanks a lot of everyone!



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