Almost Regular Matrices

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Abstract

The Silverman–Toeplitz theorem is a well-known theorem that states necessary and sufficient conditions to transform a convergent sequence into a convergent sequence leaving the limit invariant. This idea was extended to RH-regular matrices by using the notion of P-convergence (see Hamilton in Duke Math. J. 2:29–60, 1936 and Robinson in Trans. Am. Math. Soc. 28:50–73, 1926). In this chapter, we use the notion of almost convergence to define and characterize almost conservative, almost regular, strongly regular, and almost strongly regular four-dimensional matrices.