Is every matrix similar to a Toeplitz matrix?

D.Steven Mackey, Niloufer Mackey, Srdjan Petrovic
<span title="">1999</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="" style="color: black;">Linear Algebra and its Applications</a> </i> &nbsp;
We show that every n × n complex nonderogatory matrix is similar to a unique unit upper Hessenberg Toeplitz matrix. The proof is constructive, and can be adapted to nonderogatory matrices with entries in any field of characteristic zero or characteristic greater than n. We also prove that every n × n complex matrix with n ≤ 4 is similar to a Toeplitz matrix.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="">doi:10.1016/s0024-3795(99)00131-7</a> <a target="_blank" rel="external noopener" href="">fatcat:uffivojszzewfcm6x6cj2y5vla</a> </span>
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