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
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 matrix
The 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 matrix
The 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  for more details.