Is there a way to encode an instance of Subset Sum or the Number Partition Problem so that a (small) solution to an integer relation yields an answer? If not definitely, then in so …

Let $\rho$ be irreducible representation of group $G$. How one can characterize all subgroups $H< G$ such that $\rho$ can be embedded into permutation representation $F^X$, wh …

I feel like many of the algorithms that I learned — indeed, that I have taught — in undergraduate linear algebra classes depend sensitively on whether certain numbers a …

Is the (algebraic) span a finite set of vectors in a Hausdorff topological vector space over a complete field always closed? I suspect yes, but I can't come up with a proof, and i …

$A:R^n\to R^m$ be a matrix. How do I find a matrix $F:R^m\to R^n$ such that $FA=0$? ie Find $F$ such that $Im(A)=Ker(F)$.Is there any process to do this?

LLL and other lattice reduction techniques (such as PSLQ) try to find a short basis vector relative to the 2-norm, i.e. for a given basis that has $ \varepsilon $ as its shortest v …

If A and B are square matrix such that AB = I where I is identity matrix. Show that BA = I. I do not understand anything more than the following. Elementary row operations. Linea …

Suppose we have a set of quadratic forms $Q_i (x_1, \dots, x_n)$ for $1 \leq i \leq k$ in $n$ variables, defined over $\mathbb{R}$. We suppose these are 'collectively nondegenerat …

Hello everybody There is a nice classical result in linear algebra: if $A, B$ are two matrices in $M_n(k),$ where $k$ is a field, and $B$ commutes with every element of $M_n(k)$ w …

The von Neumann-Halperin [vN,H] theorem shows that iterating a fixed product of projection operators converges to the projector onto the intersection subspace of the individual pro …

I am interested in representing an arbitrary charge density (say, of atoms in a molecule) $\rho(r), \; r\in \mathbb{R}^3$ by a finite linear combination of basis functions $\rho(r …

I would like to solve a series of linear systems Ax=b as quickly as quickly as possible. However, the systems are related. Specifically, each matrix A is given by: cI + E where E …

I have been told that the study of matrix determinants once comprised the bulk of linear algebra. Today, few textbooks spend more than a few pages to define it and use it to comput …

Edit: the original poster is Menny, but the question is CW; the first-person pronoun refers to Menny, not to the most recent editor. I'm doing an introductory talk on linear alg …

Suppose k is a field and V a vector space over k. If b is an alternating nondegenerate bilinear form in V, it has a symplectic basis. A symplectic basis is a basis where the basis …