1
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1answer
47 views

Meaning of the characteristic polynomial of a matroid

From wikipedia The characteristic polynomial of a matroid $M$ (which is sometimes called the chromatic polynomial,[29] although it does not count colorings), is defined to be $$ p_M(\lambda) ...
2
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3answers
33 views

Performing matrix chain multiplication by hand

I'm trying to gain intuition for writing a matrix chain multiplication algorithm by working through a few problems by hand. I see plenty of worked-through solutions on sets of three or four solutions, ...
0
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0answers
25 views

How can I understand 3d matrix coordinates in computer science

I know calculus but I have never ever touched on matrix...so I am always clueless. I get how you can multiply 2 matrices..but what you are getting even has mathematical significance is a mystery to ...
3
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0answers
77 views

A problem on 0-1 matrices.

Given a 0-1 matrix $A$, is there an efficient way to find all 0-1 vectors $x$ such that $Ax = v$ where the entries of $v$ belong to a set $\{a,b\} \subseteq \mathbb{Z}$ of size $2$? Note that $v$ is ...
1
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1answer
71 views

texture mapping from a camera image to a 3D surface acquired by a kinect

I have the following problem: A kinect camera capture a 3D surface and save it as a .obj files containing all the positions of the vertices (in the kinect coordinate system). If I take a picture ...
0
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1answer
21 views

Homogeneous Arrays

I have this problem for homework and was wondering if anyone could help me out with it:
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0answers
27 views

Given a N*M matrix determine the number of pairs that exist in a GLCM

This is an interesting problem for which I can't find a direct solution. Given a n*m matrix (in this case 5*5): 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 There exist a certain number of ...
2
votes
1answer
91 views

Texture mapping from a camera image (knowing the camera pose)

I'm not sure if I should ask this question here or on stackoverflow, so forgive me if I'm wrong. I want to apply a texture (taken from a camera) on a 3D surface, let me explain my problem: I have ...
0
votes
1answer
57 views

Are these equivalent representations (labelled graph and adjacency matrix)?

This is an example from Wikipedia's page on adjacency matrices, which from the site's format seems to be suggesting equivalence between the simple diagram below, left, and the abstractly represented ...
0
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1answer
121 views

A an nxn matrix. P a permutation matrix that permutes columns of A. How many operations does P*A involve?

Essentially, I am supposed to count how many operations a particular computational algorithm involves, and I've gotten stuck on this one part. My understanding is that for two nxn matrices, matrix ...
0
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0answers
44 views

Deriving the fundamental equation relationship

I'm having a hard time understanding how a few equations are being derived. So the fundamental equation is an equation that relates corresponding points in stereo images. Anyway, that's the basic ...
0
votes
1answer
459 views

DCT and Inverse DCT Formulas

I'm implementing DCT, but I don't see the difference with the Inverse DCT formula. Both formula are on the Wikipedia page. The difference looks to be the normalization factor, but I don't see how to ...
4
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1answer
273 views

Matrix Chain Multiplication?

The following are questions about using dynamic programming for matrix chain multiplication. Pseudocode can be found in the Wikipedia article on matrix chain multiplication. 1) Why is the time ...
2
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3answers
5k views

Inverse of transformation matrix

I am preparing for a computer 3D graphics test and have a sample question which I am unable to solve. The question is as follows: For the following 3D transfromation matrix M, find its inverse. Note ...
1
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2answers
258 views

Understanding Matrix Formula with Scant Knowledge of Linear Algebra

$n$ is a power of $2$. $M =\pmatrix{ 1& x_0 & x_0^2 & \dots &x_0^{n-1}\\\ 1& x_1 & x_1^2 & \dots &x_1^{n-1}\\&& \vdots\\1& x_{n-1} & x_{n-1}^{2} ...
2
votes
1answer
123 views

Security analysis of a matrix multiplication protocol

Suppose Alice would like to obtain the product of two $m\times m$ matrices i.e. $A$ and $B.$ Alice has $A,$ whereas Bob has $B.$ Since Alice does not want to reveal $A$ to Bob, she chooses a ...
0
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0answers
97 views

Convert triangular real matrix to hermitian

We are developing some computer program which at some point uses a library (for which we do not have access to its source code) to solve the general eigenvalue problem; given two input real symmetric ...
1
vote
1answer
104 views

Help with the mathematical representation of operations on a matrix

I need to know how to represent the following as a mathematical formula using proper math notation: I have a $1\times n$-matrix of $3$-tuples $[a, r, x]$. I need to represent the following logic ...
2
votes
1answer
267 views

Finding equivalent matrix product of a simple quantum circuit

I was reading some papers on the efficient simulation of quantum circuits where the gates are restricted to Clifford circuits (Hadamard, PHASE and CNOT gates) and was curious about the following ...
5
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1answer
348 views

Rank of an interesting matrix

Lets define: $U=\left \{ u_j\right \} , 1 \leq j\leq N= 2^{L},$ the set of all different binary sequences of length $L$. $V=\left \{ v_i\right \} , 1 \leq i\leq M=\binom{L}{k}2^{k},$ the set of ...
8
votes
1answer
501 views

Incremental calculation of inverse of a matrix

Does there exist a fast way to calculate the inverse of an $N \times N$ matrix, if we know the inverse of the $(N-1) \times (N-1)$ sub-matrix? For example, if $A$ is a $1000 \times 1000$ invertible ...
1
vote
1answer
203 views

Rank of a graph matrix

$G$ is a bipartite graph with $2m$ nodes on the left $(u_0..u_{2m-1})$, and $2^{m}$ nodes on the right $(v_0..v_{2^{m}-1})$. There is an edge (connection) between $u_i$ and $v_j$ iff $(i+1)$'th ...
4
votes
1answer
464 views

How do you do a cross product of two $3 \times 3$ boolean matrices?

I have two boolean matrices: A = |1 1 0| |0 1 0| |0 0 1| and B = |1 0 0| |1 1 1| |0 0 1| What is the result of A x B and what are the steps ...