Let C be a (n+t)x(n+t)

square matrix. Suppose each row of ciphertext matrix C is a ciphertext produced by the above basic encryption scheme under the (n+t)xt secret matrix S.

In general, the system of linear equations in max-plus algebra will have no solution, if A is

square matrix or if the number of columns in A is more than the number of rows in A.

The

square matrix A = {[a.sub.ij]}, i, j = [bar.1,n] is called an M-matrix, if it is non-singular, [a.sub.ij] [less than or equal to] 0, as i [not equal to] j and all the elements of matrix [A.sup.-1] are nonnegative (we denote it as [A.sup.-1] [greater than or equal to] 0).

Structural equivalence was generated through a

square matrix of dyads that reveals how similar the position of a focal actor (ego) is compared to others in terms of the pattern of connections.

One can be certain about the existence of the solution when

square matrix [K.sub.e] has one of the following properties [11]:

BA = ([d.sub.ij]) is a

square matrix of m order, where [d.sub.ij] = [[summation].sup.n.sub.k=1] [b.sub.ik] [a.sub.kj], i, j = 1, 2, ..., m:

(v) S is a

square matrix, of size m, which consists of diagonal values, each equal to the sum of rows, elements of matrix M, and zero elsewhere:

The topogenous matrix [T.sub.X] = [[t.sub.ij]] associated to X is the

square matrix of size n x n that satisfies:

where [cross product] denotes Kronecker product, vec{x} is the vectorization operator which when it is applied on a given

square matrix C [member of] [C.sup.mxm], it concatenates its columns in a column vector [m.sup.2] x 1 such that

For symmetric and

square matrix, [Cxx.sup.T] = Cxx and [Cyy.sup.T] = Cyy

A complex reflection [tau] [member of] G(r, n) is associated with a

square matrixHuawei magic cube ONT is a

square matrix which can stand upright or lie flat on a desktop.