Abstract:
A matrix $A \in M_n(\mathbb{C})$ is said to be unitarily transposable if
$$
A^T=Q^*AQ
$$
for a certain unitary matrix $Q$. Every $2\times 2$ matrix is unitarily transposable; however, for greater orders, a similar statement is false, and the general description of unitarily transposable matrices of order $n$ is at present unknown. We give such a description for matrices of order three.
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