Let A = (ank) and x = {sn} (n,k = 0,1,2, … ) be a matrix and a sequence of complex numbers, respectively. We write formally
(1.1)
and say that the sequence x is summable A to the sum t or that the A matrix sums the sequence x to the value t if the series in (1.1) converges and
exists and equals t. We say that the matrix A is regular provided it sums every convergent sequence to its limit.