 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2022/digital-systems-linear-algebra-introduction-to-formal-proof-resit/6/c/i/solution

B^{k} = 0

with

k \geq 1

, put

S = I + B + \dots + B^{k - 1}

(I - B) S = S (I - B) = I - B^{k} = I .

Thus $I - B$ is nonsingular, and

(I - B)^{- 1} = j = 0 \sum k - 1 B^{j} .

∥ B ∥ < 1

is required.

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