Tagged Questions
2
votes
1answer
44 views
Could a subspace of a normed linear space be not a linear subspace?
On page 38, Functional Analysis, Pater Lax:
Let $X$ be a normed linear space, $Y$ a subspace of $X$, The closure of $Y$ is a linear subspace of $X$.
But on Wikipedia, linear subspace
A ...
0
votes
1answer
34 views
What is a “rotated” basis?
My text (p. 19) introduces the concept of a "rotated" basis without explanation. What properties or characteristics of a basis make it "rotated" with respect to another? What operation on one basis ...
1
vote
1answer
283 views
Why are vector spaces sometimes called linear spaces?
I have never come across the term 'linear space' as a synonym for 'vector space' and it seems from the book I am using (Linear Algebra by Kostrikin and Manin) that the term linear space is more ...
2
votes
0answers
58 views
Simple linear operator?
From Wikipedia
a linear operator T on a finite-dimensional vector space is semi-simple if every T-invariant subspace has a complementary T-invariant subspace.
I wonder if there is a concept for ...
2
votes
2answers
570 views
Relation between Interior Product, Inner Product, Exterior Product, Outer Product..
Following my previous question Relation between cross-product and outer product where I learnt that the Exterior Product generalises the Cross Product whereas the Inner Product generalises the Dot ...
2
votes
1answer
693 views
Relation between cross-product and outer product
If inner products ($V$) are generalisations of dot products ($ \mathbb{R}^n$), then are outer products ($V$) also related to cross-products ($ \mathbb{R}^3$) in some way?
A quick search reveals that ...
2
votes
1answer
142 views
Is there a name for this $k$-fold vector product?
Let $V$ be a set of vectors of length $n$. Define a $k$-fold product on $V$,
$$
\Upsilon(\{v_1,\ldots,v_k\}):=\sum_{j=1}^n\prod_{i=1}^k v_{ij},
$$
where $v_i\in V$ and $v_{ij}$ is the $j^\text{th}$ ...
1
vote
1answer
153 views
What is an honest basis?
In a comment to this question, the commentator stated that
"the monomials form an honest basis for your vector space".
To be honest, I never heard of that. Is this something elementary?
0
votes
3answers
92 views
What do I call a unit vector parallel to a coordinate axis?
What do I call an arbitrary element of this set of vectors?
$$
\begin{align*}
\{&\langle 1, 0, 0 \rangle, \\
&\langle 0, 1, 0 \rangle, \\
&\langle 0, 0, 1 \rangle, \\
&\langle ...
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 $a,b$) ...
1
vote
0answers
28 views
Name this concept: Comparing equal sized vectors vs. comparing features
If you obtain a vector by taking $n$ discrete samples over some underlying function, then it's easy to compare that vector with another of the same size. With a bunch of $n$-dimensional vectors, you ...
6
votes
1answer
167 views
What is the term for the projection of a vector onto the unit cube?
Normalizing a vector sets its magnitude to $1$ and retains its direction. In three dimensions, it projects the vector onto the unit sphere.
Is there a term associated with projecting it onto the ...
1
vote
1answer
158 views
Is there any math operation defined to obtain vector $[4,3,2,1]$ from $[1,2,3,4]$?
I mean have it been studied, does it have a name?
Like Transpose, Inverse, etc.. have names.
I wonder if the "inversion" of the components position have a name so then I could search material on ...
1
vote
1answer
62 views
Dimension and size of an array, matrix, vector
For a $1 \times n$ or $n \times 1$ vector, I remember people say it
is n-dimensional.
For a $n \times m$ matrix, I heard it is said to have size $n \times
m$. As to its dimension, quoted from ...
