Tagged Questions

4
votes
1answer
99 views

Every conic in $\Bbb{P}^2$ equivalent to $XZ - Y^2$ - what is meant by hint here?

I am looking at Miles Reid's UAG book. There he claims that every projective conic is projectively equivalent to $XZ = Y^2$. He asks to show that $Q$ a non-degenerate quadratic form is such that ...
0
votes
1answer
255 views

Angle between two coordinates(latitude, longitude) from a position on earth

Suppose I am standing at latitude, longitude $(-33, 151)$ and I want to calculate the angle between two points $(-32, 150)$ and $(-34, 152)$ from my point of view. Can someone please tell me how can I ...
1
vote
1answer
61 views

Change of coordinate matrices

Find the change of coordinate matrices: Wherein B is the standard basis for P2 $$B' = (t^2+2,t+3,t^2+t+1) \\B" = (2t^2+t+1, t^2, 2t+1) \\ B= (t^2,t,1) $$ $$P_{B'B}$$ means the transformation for the ...
0
votes
1answer
83 views

Transformation of a matrix, change of basis

Find the change of coordinate matrices: Wherein B is the standard basis for P2 $$B' = (t^2+2,t+3,t^2+t+1) \\B" = (2t^2+t+1, t^2, 2t+1) \\ B= (t^2,t,1) $$ $$P_{B'B}$$ means the transformation for the ...
1
vote
1answer
48 views

Test of handedness

I'm reading a book on linear algebra, where the author gives a method to test the handedness or chirality of a given set of 3 basis vectors. if (v1 x v2) . v3 > 0 then it's right-handed, while if ...
1
vote
1answer
44 views

Triangle and parametric coordinates

I'm studying on a book where it says: "A triangle is the set of points where for some point po, where u and v range over the parametric coordinates (we are talking about barycentric coordinates ...
0
votes
1answer
50 views

Zooming to an arbitary point [closed]

Maybe its a programming question, but im more interested the mathematical theory behind it. I try to zoom to a given point (mouse cursor). just like google map. (here is the visualization: ...
0
votes
1answer
36 views

parabola in homogeneous coordinates

So if I have the parabola Y = X^2, how do I go about representing this homogeneously? I know I can parameterize it as F(t) = (t, t^2), but then what? The reason I ask is because I have a 3*3 matrix ...
0
votes
3answers
52 views

Doubt on subspace of a vector space

I am new to linear algebra and I have a doubt that : in 2D coordinate system is a line which is at 45 degree NOT passing through the origin a subspace of the vector space comprising the whole 2D plane ...
0
votes
2answers
85 views

Equation of a line in homogenous coordinates given 2 points in affine coordinates

So if I have 2 points $A$ and $B$ such that $F(A) = (1; a, a^3)$, and $F(B) = (1; b, b^3)$. how do I find the equation of this line in homogeneous coordinates? So I know how to get a line the ...
1
vote
0answers
21 views

Stochastically sampling a range of UV's

Math newbie here. I am having some difficulties figuring out how to stochastically sample a range of UV points. example: [ (u,v) | v <- [5..-5], u <- [-7..7] ] I would need to make sure this ...
4
votes
0answers
226 views

Is the “Constant Rank Theorem” the same as the “Domain Straightening Theorem”? Which theorem is which?

Wikipedia says that the inverse function theorem is a special case of the "constant rank theorem". I'm pretty sure this is supposed to be the same theorem as the "Rank Theorem" on p. 47 of Boothby ...
1
vote
4answers
100 views

How to determine the position of neighbor points?

I have two points (red points represented on the image below), they form a line that have a specific formula (y = mx + n), I need to determine the coordinates of 4 other points (blue points) that are ...
1
vote
3answers
107 views

How do I calculate a change of coordinates given two lines as new axis?

Suppose we have an old coordinate system using the variables $x$ and $y$. We are given two equations for lines to form the axis for new coordinates. e.g. The line $z=0$ is given by the equation $y = ...
0
votes
2answers
50 views

Is there a simple way of arriving at this solution?

Suppose we are given the matrix $$\begin{pmatrix}x'\\y'\end{pmatrix}=\begin{pmatrix}\cos(\omega t)& -\sin(\omega t)\\\sin(\omega t)& \cos(\omega ...
1
vote
1answer
107 views

Movement in a grid

I am in a middle of a grid of 8X8 . Each box of grid is a square with side of 80 units. Suppose my current coordinates are 594,422 . How many boxes will i have to move to enter the square that ...
5
votes
2answers
170 views

Question about the nature of coordinate systems

I couldn't really think of a good one line title for my question, so I will try to elaborate. From what I have sort of gathered over my years, if you want to locate an arbitrary point in an ...