Tagged Questions

0
votes
1answer
161 views

Deriving the fundamental equation (with regards to computer vision)

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, t …
3
votes
1answer
138 views

Symplectic block-diagonalization of a real symmetric Hamiltonian matrix

Given a $2n\times 2n$ real, symmetric, Hamiltonian matrix $W$ (anticommutes with the symplectic metric), is there an orthogonal, symplectic matrix $R$ such that $R^\top WR$ is bloc …
1
vote
0answers
96 views

Calculation Camera Transformation with XYZ and UV Pairs

Hello, i have broken down my problem to plainmath and could really use some help. Basis: I have an image. In this image I have several UV-XYZ pairs. So i know the 3d position of s …
5
votes
1answer
224 views

Solve equation with matrix variable

I want to solve a matrix $\Omega$ from a equation $\sum_k (\Omega + \Theta_k)^{-1} = Q$. The $Q$ and $\Theta, \forall k=1...K$ are known, and are positive definite matrices. $\Omeg …
1
vote
0answers
68 views

Finding lower triangular matrix of an indefinite matrix

So I have the system $M = RS = RQQ^{-1}S $ and I have $R$ and $S$ currently. I impose some constraints on $R$ in the form of $r^T$$QQ^Tr = 1$ where $r$ and $r^T$ are rows of R an …
0
votes
1answer
272 views

Minimum norm solution of a least squares using SVD

Let $A$ and $B$ be any real matrices. I would like to find the solution of a linear system $Ax=B$ using the SVD decomposition of $A$ given by $A = U S V^t$. If I am not very wrong, …
3
votes
2answers
318 views

Is there a simple relation between the entropy of a matrix and its characteristic polynomial?

Assume $M$ is an invertible positive matrix of rank $N$. The Von Neumann entropy $H$ of a matrix $M$ with eigenvalues ${ \lambda_n }$is $H[M] = -\sum_{n=1}^N \lambda_n \ln \lambd …
0
votes
0answers
104 views

linsolve derivative

Consider a vector $\mathbf{g} \in \mathbb{R}^{m}$ and a matrix $\mathbf{A} \equiv \mathbf{A(g)} \in \mathcal{M}_{p\times q} [\mathbb{R}]$, a function of $\mathbf{g}$. Furthermore …
1
vote
1answer
238 views

How many zero-constraints can be added to a subspace-restricted matrix before no solution exists?

I'm trying to develop an estimator for the concentration matrix of a Gaussian Graphical Model. I've become stuck in trying to find conditions for the estimator to exist. I have a …
1
vote
2answers
493 views

Recovering a Matrix After Multiplication By Its Transpose [closed]

Given an arbitrary symmetric N-by-N matrix A, how can its original values be calculated from $P$? $$ P = A'A$$ Both $A$ and $P$ have \( \frac{N^2-N}{2}+N \) degrees of freedom. …
-2
votes
1answer
263 views

Multiplying matrix by itself [closed]

Hi There is any generic mathematical expression (formula) to represent a Matrix squared ? I search it before, but i didn't find. thanks http://www.youtube.com/watch?v=EnrIQrTsu …
1
vote
2answers
181 views

Does integral of A^T(t)*A(t) converge if det(A(t)) does not converge to 0?

Suppose you have an nxn parametric square matrix A(t). I am wondering if I can prove this: $(lim_{t\rightarrow\infty}det(A(t)) \ne 0) \Rightarrow (\int^{\infty}A^T(t)A(t)dt$ Does …
3
votes
2answers
503 views

Is there some algorithms for solving non-linear matrix equations?

Is there some algorithms for solving non-linear matrix equations on field $\mathbb{C}$? Especially, solving polynomial nonlinear matrix equations. For instance, let $X$ be some m …
0
votes
0answers
126 views

Matrixes Question [closed]

Hi, Ok so i have this question i have have some problem solving (I've done A) We have two nxn matrixes A and B and it says that A=I-AB question part A: prove that A is regular …