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. In other words, these are the spaces where we ...
2
votes
1answer
29 views
proof that intersection of two conic sections will intersect at at least two points.
In the following equation ρ(x,y) returns a constant value for a given coordinate.
n is the normal vector to the surface of the form [P,Q,-1] and s is a direction vector.
Using s = [Sx,Sy,Sz], the ...
1
vote
2answers
25 views
Is the linear dependence test also valid for matrices?
I have the set of matrices
$
\begin{pmatrix}
1 & 0 \\
0 & 0 \\
\end{pmatrix}
$
$
\begin{pmatrix}
0 & 1 \\
0 & 0 \\
...
0
votes
2answers
23 views
what is disjoint vector spaces
i want to clarify what does represent disjoint vector space?
i know that this terminology related to set is very easy,because disjoint set is for example given two set
$A={1,2,3}$
and
...
2
votes
1answer
70 views
How to prove this claim?
For $x=(x_1,\dots,x_p)$ define two norms $\|x\|_1=|x_1|+\cdots+|x_p|$ and $\|x\|=\big(\sum_{i=1}^{p}x_{i}^{2}\big)^{\frac{1}{2} }$. Find the largest constant $a>0$ and the smallest constant ...
0
votes
0answers
42 views
Calculating where somebody looks at in a room
I'm programming a computer game and unfortunately I have not got the calculation of a vector in school.
I need to calculate where somebody looks at. The area, where the player is, has got 3 ...
2
votes
2answers
30 views
Picard iterations of a matrix
I need help with this problem. I think i got the first three questions of the exercise, but i'm stuck at the fourth one.
We consider the map $T:{\mathbb{R}^2}\longrightarrow{\mathbb{R}^2}$ defined ...
0
votes
0answers
15 views
Predict binary occupancy vector from history of vectors
I have a set of binary vectors where each vector represents one day of occupancy in a house and consists of 48 elements (each element for 30 minutes of the day). Each element can be 1 meaning that ...
0
votes
0answers
17 views
Vector similarity for prediction
I have vectors of same length consisting of 1 and 0. I am trying to find out how similar they are. So far I am using hamming distance that I calculate sum of one vector then sum of second vector and ...
0
votes
2answers
38 views
Volume of a parallelepiped, given three vectors
I want the volume of a parallelpiped and I have the three vectors $$4e_1+2e_2-e_3$$$$e_1-3e_2-2e_3$$$$2e_1-e_2+3e_3$$ that coinciding with three of the parallelpipeds sides. HON-base
I made it into a ...
0
votes
1answer
30 views
Find 2 point with same distance from A
I have a math problem. I have location (x,y) of point A, B, and a number (x). I want to calculate the location of point C, D. CD is perpendicular with AB and AC = AD = x.
This is the picture describe ...
-2
votes
0answers
42 views
Number of linear maps is less or equal than the dimension of the vector space
Problem
Let $V$ be a vector space of dimension $n$. Let $T_1,T_2,\dots,T_m$ be linear maps $V\rightarrow V$ such that $\dim R(T^{2}_{i})=\dim R(T_i)=1$ for all $i=1,2,\dots,m$, and $T_i\circ T_j$ is ...
0
votes
1answer
27 views
How do I find the euler angles if I already have start and ending vector?
I have two orthonormal bases and I need to find the rotation angle over every axes to go from the first to the second one. These are my base vectors:
$$
E_1 =
\begin{bmatrix}
-0.7969 & 0.1778 ...
-4
votes
0answers
68 views
Midterm Results: Linear Algebra (Retrospective Review) [closed]
$\diamond$ How does my professor know that $V'\subset N(T+S)$ suffices to show $\Omega$ is a subspace of ${\cal{L}}(V,W)$?
Find all real numbers $a\in \mathbb{R}$ such that the set ...
1
vote
0answers
17 views
Is the polar decomposition useful in the real case as well?
I'm reading Roman's Advanced Linear Algebra p.252, where he talks about the Polar Decomposition. He states the theorem only for the case of $V$ a complex inner product space. Wikipedia also states the ...
0
votes
0answers
38 views
How to normalize a set of vectors
I have a set of vectors $\displaystyle a_1, a_2,...,a_n$ and each of which has a dimension of $k$. How can I normalize the elements of these vectors to make them lie within $[0,1]$?
I was thinking ...
