I am trying to show that: Given 2 complex non-singular matrices $A$ and $B$, there exist two unitary matrices $Q$ and $Z$ s.t. $Q^*AZ$ and $Q^*BZ$ are simultaneously upper triangular.
Thank for your help.
2026-03-25 03:18:18.1774408698
Unitary transformation to triangularize 2 matrices at the same time
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If you need a proof of this statement, it can be found in the paper G.W. Stewart, On the Sensitivity of the Eigenvalue Problem A x= Bx, SIA M J. Numer. Anal. 9, 1972, 669-686, Theorem 3.1.