# linear algebra – Recurrence relation in matrices Answer

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linear algebra – Recurrence relation in matrices

I’ve the next recursive sequence:

$$Z_k = Z_{k-1} – AA^TZ_{k-1}xx^T$$ the place $$Z_k in mathbb R^{n occasions d}, A in mathbb R^{n occasions d}, d > n, rank(A) = n, x in mathbb R^{d occasions 1}$$

$$A$$ is a ceaseless matrix, $$x$$ is a ceaseless vector. Theoretically, this sequence of matrices $$Z_k$$ is fully clear by $$Z_0$$ the preliminary component of the sequence.

If I offer you $$Z_0$$ you’ll be able to discover $$Z_k$$ for any $$okay$$.

Suppose I wish to discover $$Z_{100}$$. Is it workable to seek out an expression for $$Z_k$$ as a duty of $$Z_0$$ in order that I do not even have to seek out $$Z_1, Z_2, …, Z_{99}$$?

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