#11. Checking Matrix Multiplication

Published

12 Nov, 2023

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Prompts for discussion:

  1. Can we extend this method to distinguish between situations when \(C\) is “very close” to \(A \times B\) vs when \(C\) is “far” from \(A \times B\), for a suitable notion of distance between matrices?

  2. Let’s say the Matrix Wizard always outputs \(I_n\) and you are always multiplying two permutation matrices. Is it possible to count, in terms of some aspect of the permutation represented by \(A \times B\), the number of vectors \(\mathbf{x}\) for which \(D \mathbf{x} \neq 0\)?