29 we cannot show z n 1 converges by assuming z n is

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We cannot show Z n 1 converges by assuming Z n is always nonsingular and converges in probability to a matrix A unless A is nonsingular. As a simple example, Z n 1 0 0 n 1 1 0 0 0 A but Z n 1 1 0 0 n does not converge. 30
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