… k-separability to almost k -separability. Roughly speaking, a matrix is almost k -separable if
… Our main result shows that it is possible to achieve almost separability with only \(O(k \log n)\…

… Moreover if we say that a specific part of a matrix is of semiseparable form, it means that this
… the vectors u and v to try to compensate the fact that the matrix is almost block diagonal.10 …

… or not and how to check if a matrix is separable or not. We propose … To check the separability
of a matrix, we construct a … In other words, Algorithm 4.2 is almost always able to check the …

… F is a closed, non-separable subspace of :~, invariant … A matrix is called almost Schur
provided that A (/~) _ F. It is the purpose of this section to characterize the almost Schur matrices. In …

… Let B be a given m × n matrix that can accurately be approximated by a matrix of rank k, and
suppose that we seek to determine a matrix Q with orthonormal columns (as few as possible…

… Given an n×t 0,1 matrix Ω , we define Ω(m,p,t) to be the (m+n)×t matrix that results from
adding m random rows r i with 1⩽i⩽m to Ω . We let ω j with 1⩽j⩽n be the jth row vector of Ω . We …

… + 1)-separable matrix based on an α-almost k-disjunct matrix … the complement of such a
matrix with a set of random rows. The … of an α-almost ke-disjunct matrix and similarly construct an …

… compensate the fact that the matrix is almost block-diagonal. … banded plus semi-separable
matrices. Linear Algebra and Its … diagonal plus semi separable matrices to tridiagonal and …

… of independent columns of a generator matrix the corresponding set of … set, the code has a
unique generator matrix of the form … identity matrix; such a generator matrix is in standard form …

… Suppose we have a partly filled p x q data matrix Y of quantitative observations, most often
… When studying the results, we first notice that in almost all cases Algorithms I and II are …