Given a matrix $M$ of size $n\times n,$ we write its different eigenvalues by $x_1,x_2,\ldots,x_m$ with $m\leq n$ such that $|x_1|>|x_2|>|x_3|>\cdots|x_m|,$ and call $x_2\doteq |\l …

In the pinhole camera model, I can get the homography 3x3 matrix of two images. My problems is: provided an camera intrinsic matrix(the projection matrix), can I find the find the …

A unimodular matrix $M$ is a square integer matrix having determinant $+1$ or $−1$. A totally unimodular matrix (TU matrix) is a matrix for which every square non-singular submatr …

I have a real supermodular objective function which I want to maximize with constraint. The constraint is on the size, like |A|=k . I am wondering if anyone can give me more inf …

There are $k$ points placed inside a polygon and I am interested in finding a point inside the polygon (not necessarily on its boundary) who's minimum distance to any of the $k$ po …

Conventions: A polytope in a finite-dimensional $\mathbb R$-vector space $V$ is defined to be a convex hull of finitely many points in $V$. A polyhedron in a finite-dimensional $\m …

Hello, My question regards to the Schur complement lemma. Consider the matrix $M=\left( \begin{array}{cc} A & B\\ B^T & C \end{array}\right) $. According to the lemma $M\ …

I have a problem minimizing sum of piecewise linear functions. Given $f:R\rightarrow R$ with $f(x) = \sum_{i=1}^n \max (a_ix,b_ix+c_i)$ and $a_i,c_i <0; b_i>0$ find an equation …

Given the primal objective $$F({\bf a})=L\sum_{i,j}a_{i}a_{j}k(x_i,x_j) + \sum_{i}max(0, 1-y_i \sum_{j}a_jk(x_i,x_j)$$ for the soft margin SVM, where ${\bf a}=(a_1,...,a_N)$, N be …

I have a problem that necessitates solving a large non-negative least-squares problem. My matrix A is large, sparse, highly rectangular (num rows >> num cols) and nearly binary. …

I have the equation $\Sigma_k(M_k{p_k})V=EV$, where the $M_k$ are n*n real Hermitian matrices, $V$ is a n*n eigenvector matrix, $E$ a dim-n energy eigenvector and the $p_k$ scalar …

The Gauss-Newton algorithm optimizes functions $$ E(x) = \sum f(x)^2 $$ by approximating f as (locally) linear, in which case the Hessian of $E$ is approximated as $$ H = 2 \sum …

I would be grateful for pointing me out a reference to some general bound on the $\ell_{\infty}$ norm of a solution of a linear system. To be specific, suppose that we have an unde …

Suppose $x \in \mathbb{R}^n$, $B,U \in \mathbb{R}^n\times\mathbb{R}^n$ and $U$ a unitary matrix. Define $g_{U}(x) = || BUx||$ where $||.||$ is some norm or norm-ish function on $\ …

What is the dual of a norm that is the sum of two-norms? Specifically, say we have the following norm for $\mathbf{x}\in \mathbb{R}^n$ and $\mathbf{A}_i \in \mathbb{R}^{m \times n} …