Questions tagged [map-projections]

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40 questions
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Surjectivity of a complex projection

Given is the projection $$u: \mathbb{C} \rightarrow \mathbb{R}: z \rightarrow Re(|iz|) - |iRe(z)|$$ which is $$u: \mathbb{C} \rightarrow \mathbb{R}: z \rightarrow |z| - |Re(z)|$$ when simplified....
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Help with surjectivity of a function

My function $f$ is as follows: $$f: \mathbb{R} \rightarrow \mathbb{R^2}: t \rightarrow (2cos(t), - sin(t))$$ Now, I'm fairly certain that the function isn't injective, as both sine and cosine are ...
971 views

What is the difference between moment projection and information projection?

Moment projection is defined as $$\text{arg min}_{q\in Q} D(p||q)$$ while information projection is defined as $$\text{arg min}_{q\in Q} D(q||p)$$. Aside from the difference in the formula, how should ...
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Difference between orthogonal projection and oblique projection physically.

Let $A$ and $B$ be $n \times n$ matrices in $\mathbb{R}^n$, $N(B)$ denotes nullity of $B$. Let $C$ and $N(B)$ are complementary subspaces of $\mathbb{R}^n$. Let $P_c$ denotes the oblique projector ...
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Are projection and norm enough to define an inner product?

Given an inner product, one can define a projection and a norm. Can we do the opposite? That is, suppose we have: a complex vector space V a norm $|V|^2 : V \rightarrow \mathbb{R}$ such that: is ...
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Converting from Mercator Projection to Latitude and Longitude

I have an image of (what I believe to be) a Mercator Projection map of Strangereal, from the Ace Combat game series. I have opened this map in GIMP and am reading pixel measurements for different ...
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Projection onto a plane

I was looking at this post ($3D$ projection onto a plane) in which the answer describes how to project a given set of points onto any arbitrary plane. However, this transformation is still of the ...
Is it related to projections as in $P P = P$?
Given a great circle connecting two points on a sphere, what is the function describing it's Mercator projection? In other words, given two longitudes and latitudes $(\phi_1, \theta_1)$ and \$(\phi_2, \...