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I want perform a simple check for total unimodularity. Question: what, if anything, can be concluded from the fact, that $$det(A)=1,\ a_{ij}\in\{-1,0,+1\}\ \wedge\ a_{ij}^{-1}\in\{-1,0,+1\}$$ wher …

Question: Given a $\pmb{A}\in\mathbb{R}^{n\times n},\ \pmb{A}^T=\pmb{A},\ \pmb{A}_{ii}=0$, is it possible, to generate via operations of linear algebra $\pmb{B}\in\mathbb{R}^{n\times n}:\ \pmb{B}_{ij …

Trying to identify canonical vertex weights for complete weighted graphs, I investigated the Ansatz, that the sum over the weights of all edges that are adjacent to same vertex, should equal the sum o …

Question: is there a special name for matrices whose rows and columns sum to zero? I actually need information about those matrices and thus a keyword for online search. Edit: as there apparently is …

Question: What are, provided their existence, examples of functions $f$ with the following properties: \begin{align}f:& \ \mathbb{N}\times\mathbb{N}\ni(i,j)&\mapsto\ \quad\quad\quad\qu …

Are there any examples, earlier than spline-interpolation, of mathematical investigations of interpolation problems with more unknowns than conditions or are (polynomial) splines the earliest? Spli …

are there any invariants of matrices, that are not affected by row- and/or column permutations? To me it seems that the sequence of singular values could be such an invariant; am I right, resp. are t …

Question: is there a name for the following operation $$\sum_{i=1}^n\sum_{j=1}^mx_iy_j^T,\ x_i,y_j\in \mathbb{R}^k$$ i.e. for generating a square matrix that is the sum of the cartesian product of a …

I accidently found a class of rank-deficient square matrices that are their own Moore-Penrose pseudo inverse: $$\boldsymbol{A}\in\mathbb{R}^{n\times n}: a_{(i,i)}=n-1,\, a_{\lbrace i,j\rbrace}=-1\impl …

Question: Are there standard techniques available for solving the following kind of linear matrix recurrence relations: $$M_1,\cdots,M_k\ \in\ \mathbb{R}^{m\times n}$$ $$ A_1,\cdots,A_k\ \in\ \mathb …

is there an established name for the property that a square matrix can be made symmetric by permutation of its columns? Is it possible to recognize those kind of matrices efficiently?

I have the problem of solving very large and very sparse least squares problems and, a bit dissatisfied with the run-times of the full-fledged QR-algorithm, I would like to bring the instances into bl …

I just found the article "Column Reordering for Box-Constrained Integer Least Squares Problems" by Stephen Breen and Xiao-Wen Chang (available online here: http://arxiv.org/abs/1204.1407), which addre …

Is there a name for linear transformations of the plane, that make $4$ points in general convex configuration co-circular, with the biggest circle through those points and, how can they be determined …

If you rewrite to $\boldsymbol{X}\boldsymbol{A}\boldsymbol{X}^T$ there is an answer here Names for the product will depend on the properties of $\boldsymbol{X}$ and $\boldsymbol{A}$