# Tagged Questions

21 views

### Linear equation so that the solutions has to be integers.

I have this equation $$-X_5-32X_4-32^2X_3-32^3X_2-32^4X_1=[PARAMETER]$$ I want to get all the solutions to this equation with a given parameter(integer) and all of the solutions has to be integers ...
38 views

### Is there any algorithm (if possible, I need the codes) for Jordan normal form decomposition for large matrices in practice?

Although it is an ill-posed problem as B Kågström said in "An algorithm for numerical computation of the Jordan normal form of a complex matrix", I wonder what people do when they need to do Jordan ...
76 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 ...
68 views

### Floating Point Number System

I really have no idea of how to do these questions - in fact I have no idea of how to do any question in the paper - but I have tried to figure out what's going on in the course called Computational ...
38 views

### Why we take transpose of Vector (Displacement Vector)?

I'm trying to understand some equations that involves transpose of vectors (displacement vectors to be precise) Two set of vectors F and G (with i,j) that corresponds to X,Y value in plane and ...
40 views

### It would be possible to use the covariance matrix $C'=XX^T$ instead of the standard $C=X^TX$ to get the same result on PCA?

It would be possible to use the covariance matrix $C'=XX^T$ instead of the standard $C=X^TX$ to get the same result on PCA? If so, what are the next steps to retrieve the data with reduced ...
68 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 ...
113 views

### How to solve this system of 3 equations with 3 variables?

I stumbled upon this system with constants $a_{i,j}>0$ that I want to solve for $x,y,z \in\mathbb{R}$: \begin{align} a_{2,1}y+a_{3,1}z=& x(y+z) \\ a_{1,2}x+a_{3,2}z=& y(x+z) \\ ...
49 views

### Computationnal geometry: vector, basis, point and coordinate system?

I am trying to build a small geometrical library in C++, that is mathematically consistent (not so false). The goal here is to construct two concepts: vectors and points. I am not sure that the ...
96 views

### Avoid dividing by zero with just variables and basic operators

I am working on stats for a sports team, and one of the stats I have the ratio of Shots and Shots on Target (Which I call ...
60 views

### Inward-pointing normal and co-ordinate systems

I'm doing a course in computer graphics, and as such, we're being taught measures on how to deal with the Hidden Surface Removal problem. One of the topics covered was "back-face detection", that is, ...
133 views

### Algorithm for obtaining the surface of a mirror

My colleague and I have been trying to implement an algorithm described in the paper "Recovering local shape of a mirror surface from reflection of a regular grid", primary author of which being ...
54 views

### Representing everywhere a camera can see as a matrix

I'm learning about Computer Graphics and there is one point really puzzling me. I understand that vertices (vectors) represent points in space and that transformation matrices represent changes that ...
578 views

### Learning Proofs (for Computer Science)

Harvard's math curriculum, for freshmen, is divided into 4 classes beyond the BC Calculus level, Math 21, 23, 25 and 55. Math 21 is your classic plug-and-chug multivariable calculus and linear algebra ...
67 views

### Can a directed hamiltonian path be found in polynomial time?

I was discussing a programming competition problem with one of my math professors in Linear Algebra that reads as follows: A matrix is an $r\times c$ array of numbers, where $r$ is the number of ...
41 views

### Solving system of linear eqaution in special cases

I have to solve for $Ax=B$. Here the diagonal elements of $A$ are $-1$ and all other elements are $1$. $A$ is $n \times n$ matrix . In this special case can we solve for $x$ quickly? EDIT: quick is ...
60 views

### Algorithm to check if a matrix is elementary

I'm currently writing a homework problem for a linear algebra course and I'm trying to come up with an algorithm to check if a matrix is elementary. That is, to check if it is one of the three forms ...
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 ...
120 views

### Maximal subset with rank $k$

I'm trying to solve the following problem for an algorithm I'm trying to develop and I couldn't find anything helpful in scholar google. Here is the question: Suppose I have a set of $N$ vectors ...
43 views

### Difficulty understanding some algebra done in a problem

The main problem is about computer science, trying to show that $f(x)=e^{x^Tx'}$ is of the form $\exp{\Big( \frac{||x - x'||^2}{2\sigma^2} \Big) }$, so it could be a kernel function. (see here for ...
83 views

### Procedures to find solution to $a_1x_1+\cdots+a_nx_n = 0$

Suppose that $x_1, \dots,x_n$ are given as an input. Then we want to find $a_1,\ldots,a_n$ that satisfy $a_1x_1 + a_2x_2+a_3x_3 + a_4x_4+\cdots +a_nx_n =0$. (including the case where such $a$ set does ...
219 views

### 0-1 knapsack like - the set of all non-contained affordable binary selections

This is my first question here, so please go easy on me :) The following problem is – I think - similar to the 0-1 knapsack problem. It's simplified somehow in that each item has only a cost ...
142 views

### Question about the elementary divisors of a special matrix

I have the following question: Is there a closed formula for the elementary divisors of the Matrix $M={(m_{ij})}_{i=1,...,n,\ j=1,...,k}$, where ${m}_{ij}$ is the greates common divisor of $i$ and ...
150 views

### Operations it takes to invert a matrix

I had this question on a homework and I was wondering if my thinking was correct. if you have a nxn matrix, how many total arithmetic operations do you perform? ( +,-, *, /)...I went about this ...
272 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 ...
379 views

### Distance between a point and a m-dimensional space in n-dimensional space ($m<n$)

I am trying to find a method with a low computational cost to compute the distance of a point $P$ and a space $S$ that is defined by the origin $O$ and $m$ vectors $v_1, v_2, ..., v_m$ in an ...
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 ...
258 views

622 views

### knapsack algorithm that looks too good to be true

I have an idea for solving the knapsack problem, but it looks too good to be true. I would like someone to explain potential problems with this approach. I'll give an example: I want to find a subset ...