We investigate the variety of commuting matrices. We classify its components for any
number of matrices of size at most 7. We prove that starting from quadruples of 8× 8 …

A phylogenetic invariant for a model of biological sequence evolution along a phylogenetic
tree is a polynomial that vanishes on the expected frequencies of base patterns at the …

Phylogenetic algebraic geometry is concerned with certain complex projective algebraic
varieties derived from finite trees. Real positive points on these varieties represent …

We prove the Box Conjecture for pairs of commuting nilpotent matrices, as formulated by
Iarrobino et al [28]. This describes the Jordan type of the dense orbit in the nilpotent …

Abstract A tuple (Z 1,…, Z p) of matrices of size r× r is said to be a commuting extension of a
tuple (A 1,…, A p) of matrices of size n× n if the Z i pairwise commute and each A i sits in the …

The problem of irreducibility of the variety C (3, n) of triples of commuting n× n matrices is
equivalent to that whether each triple of commuting n× n matrices can be approximated …

Let N (d, n) be the variety of all d-tuples of commuting nilpotent n× n matrices. It is well-
known that N (d, n) is irreducible if d= 2, if n⩽ 3 or if d= 3 and n= 4. On the other hand N (3, n) …

Approximating commuting operators Page 1 Linear Algebra and its Applications 327 (2001)
131–149 www.elsevier.com/locate/laa Approximating commuting operators John Holbrook a …

This work relates to three problems, the classification of maximal Abelian subalgebras
(MASAs) of the Lie algebra of square matrices, the classification of 2-step solvable …

We survey recent results on open embeddings of the affine space $\mathbb {C}^ n $ into a
complete algebraic variety $ X $ such that the action of the vector group $\mathbb {G} _a^ n …