Sentence examples for matrices only if from inspiring English sources

Ectoparasites and their vertebrate hosts were included within interaction matrices only if species-level identifications were available.

A matrix can have an inverse matrix only if its number of columns is equal to its number of rows.

These two relations come from the fact that the Kronecker product between any two diagonal matrices is equal to the identity matrix if and only if these diagonal matrices are (scaled) identity matrices that compensate each other.

(iii) It is a well-known result that a Hausdorff matrix is a Nörlund matrix if and only if it is a Cesàro matrix.

The matrix A is an H-matrix if and only if (langle Arangle) is an M-matrix.

Base on the essential matrix constraint [29], a 3 × 3 matrix is an essential matrix if and only if two of its singular values are equal and the third is zero.

In [16] it was proved that a B-matrix has positive diagonal elements, and a real matrix A is a B-matrix if and only if it can be written in the form (3) with (B^) being a SDD matrix.

In addition, the OSM matrix can be constructed only if the matrices representing the substitutions, the so-called substitution matrices, and the identity matrix form a commutative or Abelian group (see, e.g., [ 8]) with respect to matrix multiplication [ 4].

Theorem 1 A 4 × 4 matrix J is a Jacket matrix similar to the diagonal matrix if and only if J has the following form: J 4 = A 2 B 2 C 2 A 2 (1).

A matrix A is called an M-matrix if there exist a nonnegative matrix B and a real number s > ρ ( B ) such that A = s I − B, where ρ ( B ) is the spectral radius of B. It is well known that A is an H-matrix if and only if μ ( A ) is an M-matrix, and if A is an M-matrix, then the Schur complement of A is also an M-matrix and det A > 0 (see [3]).

The matrix A is a Metzler matrix if and only if the continuous-time system dot{x}(t)=Ax t) (2.2) is positive for any (tin 0,infty)).