The following is another definition for a d-disjunct matrix: Definition 1: H is a d-disjunct matrix iff for any (d+1) columns, there exist a row such that an entry at one of those (d+1) columns is 1 and entries at the remaining d columns are 0. We assume that a given matrix M does not contain any isolated columns since we only consider non-unique probes.
There exists a r × n matrix, called L (z ), that is a row basis for E [ Y | z ], where r ≤ n (Leek and Storey, 2007, 2008).
Definition 2. The matrix A k×n is called (m,a,b) -extendable if A is a PPM A has k nonidentical rows There exists a matrix B m×n that is a (k,a,b) -PPM, and the rows of A and B are identical.
Definition 5.2 The generalized slater condition is satisfied at x 0 ∈ S ( X ) for the SOCBLP problem (21) if B 2 is of full rank in row and there exists a y 0 ∈ int K m such that A 2 x 0 + B 2 y 0 = b 2 holds.
By analyzing the orthogonal matrix U via SVD, it is found that there exists a strong similarity correlation between the second row first column element and the third row first column element.
Lemma 1 Given an arbitrary r × s polynomial matrix D (q ) with r ≤ s and of full row rank for almost all q, there exists a unimodular left multiplying matrix such that the product is row reduced.
for any subset M of the rows of A, there exists a partition (M 1, M 2) of M such that each column q satisfies ∑ p ∈ M 1 a pq - ∑ p ∈ M 2 a pq ≤ 1. See [22].
A matrix A is totally unimodular if (i) a pq ∈{0,+1,-1} for all p, q, and (ii) for any subset M of the rows of A, there exists a partition (M 1, M 2) of M such that each column q satisfies ∑ p ∈ M 1 a pq - ∑ p ∈ M 2 a pq ≤ 1. . a pq ∈{0,+1,-1} for all p, q, and.
A (0, 1 -matrix satisfies the consecutive ones property if there exists a column permutation such that the ones in each row of the resulting matrix are consecutive.
There exists an ordering of the rows and columns of B, which yields a canonical matrix.
