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Lists, Vectors, Sequences
09-12-2019, 12:18 PM (This post was last modified: 09-12-2019 12:45 PM by Dirk.nl.)
Post: #1
Lists, Vectors, Sequences
Hey,
For discussion; I have a few questions about lists, vectors, sequences, etc.

In my experience, a vector indicates a direction and a value (mechanical / electrical).
Vectors can be presented with Cartesian, Spherical or Cylindrical. Two or three dimensional.
In the Matrix Editer you can select Vect. You can then enter as many values ​​as you want. This is presented as a column. This vector is presented horizontally in the command line.
(My HP Prime is set to textbook)

Question 1:
You would think that a vector can consist of only 2 or 3 values?
Only if it were geometric?
With multiple values, what exactly is the difference between a vector and a list?

Question 2:
Is a vector in the HP Prime (because you can enter many more values) a row vector or a column vector? Or does that not matter?

Returning to my previous Thread “Geometry App, Distance, Intersections”.
(Thanks kevin3g)

Question 3:
How can I see if a variable (or an object?) is a list or a sequence?
How are these presented in CAS?

Ps.
Take my questions for granted, I have been a retired (software) engineer / consultant for offshore pipelay barges and crane vessels (tensioners, winches and ballast control- and simulation systems) for a reasonable time. I’am getting old !! (I hope).
I did my maths study in the sixties!
I mainly use my HP Prime for my engineering hobbies. I have written several useful programs for this. This means that the HP Prime is very useful (easy to use) for engineers !!

— Dirk Hartland
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09-13-2019, 03:33 PM
Post: #2
RE: Lists, Vectors, Sequences
(09-12-2019 12:18 PM)Dirk.nl Wrote:  Hey,
For discussion; I have a few questions about lists, vectors, sequences, etc.

In my experience, a vector indicates a direction and a value (mechanical / electrical).
Vectors can be presented with Cartesian, Spherical or Cylindrical. Two or three dimensional.
In the Matrix Editer you can select Vect. You can then enter as many values ​​as you want. This is presented as a column. This vector is presented horizontally in the command line.
(My HP Prime is set to textbook)

Question 1:
You would think that a vector can consist of only 2 or 3 values?
Only if it were geometric?
With multiple values, what exactly is the difference between a vector and a list?
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:
Is a vector in the HP Prime (because you can enter many more values) a row vector or a column vector? Or does that not matter?
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”.
(Thanks kevin3g)

Question 3:
How can I see if a variable (or an object?) is a list or a sequence?
How are these presented in CAS?

I'm not familiar with sequences, so I'll let somebody else answer this one.
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09-13-2019, 05:09 PM (This post was last modified: 09-13-2019 05:10 PM by Dirk.nl.)
Post: #3
RE: Lists, Vectors, Sequences
THANKS Claudio ! Nice explanation.

— Dirk Hartland
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