Geodesic
On the Multiplicative Inverse Eigenvalue Problem
Canadian mathematical bulletin, Tome 15 (1972) no. 2, pp. 189-194

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By "multiplicative inverse eigenvalue problem" (m.i.e.p., for short) we mean the following. Let A be an n×n matrix and let s1,..., sn be n given numbers. Under what conditions does there exist an n×n diagonal matrix V such that VA has eigenvalues s1,...,s n ?In the "additive inverse eigenvalue problem" (a.i.e.p., for short) we seek the diagonal matrix V so that A + V has eigenvalues s1,..., s n ?.In the present paper we extend to the m.i.e.p. the ideas used in [7] for the a.i.e.p.By per X we denote the permanent of the square matrix X. 
Oliveira, G. N. De. On the Multiplicative Inverse Eigenvalue Problem. Canadian mathematical bulletin, Tome 15 (1972) no. 2, pp. 189-194. doi: 10.4153/CMB-1972-034-0
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     author = {Oliveira, G. N. De},
     title = {On the {Multiplicative} {Inverse} {Eigenvalue} {Problem}},
     journal = {Canadian mathematical bulletin},
     pages = {189--194},
     year = {1972},
     volume = {15},
     number = {2},
     doi = {10.4153/CMB-1972-034-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1972-034-0/}
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