Organisations and businesses represented at the meeting included Atom Bank, Barclays, Business Durham, Mincoffs, Newcastle University, the North East Combined Authority, Sage, Ryecroft Glenton, Northstar Ventures, Kani Payments and

Block Matrix.

We 'multiply the second equation in (2.7) by the complex unit number i to get the

block matrix system,

From a direct computation we observe that the matrix [mathematical expression not reproducible] is the lower triangular

block matrix of H with an additional [lambda]I on the diagonal blocks and the matrix [mathematical expression not reproducible] is the strictly upper

block matrix of H minus [lambda]I, where I is the identity matrix in [R.sup.r(I+J+K)xr(I+J+K)] The structure is given in the following formulas:

Firstly, according to Equation (11), we randomly block the measurement matrix to obtain a stochastic

block matrix (or submatrix) [[PHI].sub.blockxn], which can be expressed as

Then, based on the RQ decomposition of the Hankel

block matrix, the weighted oblique projection [mathematical expression not reproducible] can be computed.

The decompositions of the maximal subgroups of n x n tropical matrices containing an idempotent diagonal

block matrix are established in Section 3.

(1), we have the following linearized matrix equations, written in the form of a

block matrixThe linear system PX = K over Z[[Q.sub.16]] is equivalent to a linear system M(P)X = V(K) over Z, where M(P) = [M([p.sub.ij])] is a

block matrix and V(K) = [v([k.sub.1]) *** v([[k.sub.m])].sup.t] with v(q) = [[q.sub.0] *** [[q.sub.15]].sup.t] is a column vector with coordinates in Z.

where [??] = [(<f, [[phi].sub.0]>, <f, [[phi].sub.1]>, ..., <f, [[phi].sub.2n]>).sup.T] and M is the 2 x 2

block matrixThe submatrix [DELTA][H.sub.(0)] is set to a zero

block matrix to simplify the computation in accordance with the fact that the previous data is not related to the new hidden nodes.

and accepting the

block matrix structure of (21) and (24), it can define

where [C.sup.(r)] = diag([C.sub.1.sup.(r)], ..., [C.sub.m.sup.(r)]), [L.sup.(r)] = diag([L.sub.1.sup.(r)], ..., [L.sub.m+1.sup.(r)]), [G.sup.(r)] = diag([G.sub.1.sup.(r)], ..., [G.sub.m.sup.(r)]), [R.sup.(r)] = diag([R.sub.1.sup.(r)], ..., [R.sup.m+1.sub.(r)]), and E is a

block matrix of the identity and zero matrices, [+ or -]I and 0, respectively, see [15] for more details.