grandes-ecoles 2020 Q27

grandes-ecoles · France · centrale-maths1__mp Matrices Diagonalizability and Similarity

Deduce property (S): The permutation matrices $P_\sigma$ and $P_\tau$ are similar if and only if the permutations $\sigma$ and $\tau$ are conjugate.
One may compute $T_\sigma D$ where $T_\sigma$ is the cycle type of $\sigma$ and $D$ is the divisor matrix defined in I.D.

Deduce property (S): The permutation matrices $P_\sigma$ and $P_\tau$ are similar if and only if the permutations $\sigma$ and $\tau$ are conjugate.

One may compute $T_\sigma D$ where $T_\sigma$ is the cycle type of $\sigma$ and $D$ is the divisor matrix defined in I.D.

Paper Questions

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