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Questions about the properties of vector spaces and linear transformations, including linear systems in general.
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Bounding 2nd Eigenvalue of a Pseudo-Rotation-ish matrix
Let $p,q$ be arbitrary primes.
Let $N = p * q$.
Let $I$ be the $N * N$ identity matrix.
Let $R$ be the $N * N$ matrix defined as follows:
$R[x_0 * p + y_0, x_1 * p + y_1]=1$ if and only if $x_0+1 …