Tagged Questions
1
vote
0answers
33 views
To show that something is a four-vector
I hope this question is not too inane... it would be really helpful for me to have this cleared up. I want to know what I need to show to demonstrate that something is a four-vector. I have checked ...
0
votes
0answers
34 views
Find a number that minimizes distance to a vector of sets of numbers
Assumptions
$V$ is a vector of sets $V_1,V_2,...,V_n$ of numbers:
$V=[V_1, V_2,..., V_n]^T, \forall_{i=1..n}V_i\subset\mathbb{R}$
$c\in\mathbb{R}$ is constant
$d(V,c)$ is an error metric: ...
6
votes
2answers
82 views
What structure does the space of functions into $X$ (or the cartesian exponentiation of $X$) inherit from $X$?
When dealing with a space $X$, that posses a lot of structure (complete lattice, complete metric space, vector space), what can be said about the cartesian exponentiation $X^Y=\{f \mid f:Y\rightarrow ...
-1
votes
1answer
103 views
Practical implications of a vector space being a topological vector space
I have a space $V$ and I lately discovered that it's a topological vector space. What are the practical implications of that?
1
vote
1answer
32 views
Recommend a space to analyze the bearing of the vector between any two points
In Euclidean space, given any two points, the vector connecting them can be characterized by length (distance) and direction (bearing). Now I am only interested in the bearing part. And I found it is ...
0
votes
1answer
33 views
If $a=b+ c$ and $E$ is the basis of $a$, Will $E$ be also basis for $b$ and $c$?
Suppose $a$ lies in the span of a set of independent vectors $E$. Now, if $a=b+c$, is it also the case that $b$ and $c$ lie in the span o the same set of vectors $E$?
if the question is obscure, ...
2
votes
4answers
721 views
What is the difference between metric spaces and vector spaces?
Does a metric space have an origin? That is, does it have $(0,0)$.
Does a vector space have an origin?
It seems whatever you can do in a metric space can also be done in a vector space. Is this ...
1
vote
1answer
817 views
Cosine similarity / distance and triangle equation
There is a similarity function particular popular for processing sparse vectors such as textual data (word frequency counts etc.) commonly referred to as cosine similarity.
There are two variants to ...
1
vote
1answer
81 views
What is the proper term for the entity that relates a vector space and a set?
One way to generate a metric for a set $S$ (a distance function between elements $a,b$ of the set $S$) would be by associating it with a vector space $V$ (the vectors that connect the elements $a,b$) ...
0
votes
1answer
199 views
How Many Movable Ways(vector) In Pure $N$th-Dimensional Space?
In my opinion, In pure $2$th-dimensional space, There is 2 movable ways.
And in pure $3$th-dimensional space, There is 3 movable ways.
Am I think in right way?
Any answers will be appreciated, ...
12
votes
2answers
2k views
Difference between metric and norm made concrete: The case of Euclid
This is a follow-up question on this one. The answers to my questions made things a lot clearer to me (Thank you for that!), yet there is some point that still bothers me.
This time I am making ...
