Questions tagged [vector-spaces]
For questions about vector spaces and their properties. More general questions about linear algebra belong under the [linear-algebra] tag. A vector space is a space which consists of elements called "vectors", which can be added and multiplied by scalars
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Is Cross Product Defined on Vector Space?
In Wikipedia, a cross product between two "vectors" is defined in terms of the angle between the vectors and their magnitudes.
As I learned cross product in linear
algebra, which I understand to be a
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Vector space over $\mathbb{Q}$ or $\mathbb{Z}$?
I am looking at the following:
Show that a torsion-free divisible group $G$ is a vector space over $\mathbb{Q}$.
I have no problem verifying the axioms of vector spaces after noting that the term ...
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Motivation for normed space definition?
So if $X$ is a vector space, and you define a norm, $x \mapsto \| x \|$, on it, then the bounded subset, $V = \{ x \in X: \|x\| < \infty \}$ is automatically a subspace.
This follows from the ...
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Vectorspace: Is $\lambda a = a\lambda$ always true?
I just had a short look on the definition of a Vector Space and couldn't find any obvious reason why
$\lambda a = a \lambda$
where $\lambda$ is an element of the field $K$ and $a$ is an Element of ...
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How to check if a subset is a generator of a vector space
I have a very noob questions about generators: what algorithm do I have to follow so I can prove that a finite subset is a generator?
Here is the background story (I'll tell it all because I suck at ...
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Vector Force Fields and Their Physical Interpretations
The vector force field F=(yi,-xj) has a curl of -2. The acceleration of a particle in space is given by:
ax=y/m
ay=-x/m
This vector field has a divergence of 0. Will particles in this vector FORCE ...
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Getting the % that a point is on a line
Alright, so I got two points in 3d space, so they have a x,y, and z.
Now if the line's y - which I get like so:
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Finding $\min_{\mathbf x} (\mathbf y - \mathbf G\mathbf x)^T(\mathbf y - \mathbf G\mathbf x)$
Let $\mathbf G$ be a given $m \times n$ matrix, $\mathbf y$ a given $m \times 1$ column vector and $\mathbf x$ an unknown $n \times 1$ column vector such that $\mathbf x \ge 0$.
1) How do you find $\...
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Showing $1,e^{x}$ and $\sin{x}$ are linearly independent in $\mathcal{C}[0,1]$
How do i show that $f_{1}(x)=1$, $f_{2}(x)=e^{x}$ and $f_{3}(x)=\sin{x}$ are linearly independent, as elements of the vector space, of continuous functions $\mathcal{C}[0,1]$.
So for showing these ...
anonymous
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How do you calculate the unit vector between two points?
I'm reading a paper on fluid dynamics and it references a unit vector between two particles i and j. I'm not clear what it means by a unit vector in this instance. How do I calculate the unit vector ...
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Simple-looking vector inequality
For what values of $x = (x_0 x_1 \ldots x_n)$ the following inequality holds for all positive values of the vector $a = (a_0 a_1 \ldots a_n)$: $a x^T \ge 0$?
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Show that this is a vector space and determine the dimension
Question: Let $v = (1,1,0,1) \in \mathbb{R}^{4}$ Let $$V:= \{f: \mathbb{R}^{4} \rightarrow \mathbb{R}^{2} \mbox{ linear } | f(v) = 0\}.$$
(a) Show that $V$ forms a vectorspace.
(b) Determine dim$(V)...
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Let $V$ be a $k$-vector space of dimension $n$ and $T: V \to V$ a linear map of rank 1. Show that either $T^2 = 0$ or that $T$ is diagonalisable?
I am not good with vector spaces so I would be grateful for any help.
As I've been told I need to take $v \in \mathrm{Im}(T)$, $v\neq 0$, and show that if $T(v) = \mathbf{0}$ then $T^2 = 0$. But if $T(...
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Bad ideas: Adding vectors from different vector spaces?
Let V be a vector space with a non-trivial subspaces U, W. $ U \neq W$. Consider $u_0 \in V$, with $u_0 \neq 0$ and $w_0 \in V$ with $w_0 \neq 0$ then we have $u_0 + U \in V/U$ and $w_0 + W \in V/W$. ...
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