for Fig. 2. For comparison with the previous results, the leading eigenvalue is 0 . 72 ± 0 . 06. III. CONCLUSION We have analyzed the sensitivity of the low-lying spectra of the random two-body ensem- ble of interactions to variations of the Hamiltonian matrix elements; by using singular value decomposition, we find the dominant linear combinations, which would be important in any fit to experimental data. We found the SVD eigenvalues follow a pattern remarkably simi- lar to that shown by semi-realistic/semi-phenomenological interactions such as USDB. We also analyzed the most dominant linear combinations of matrix elements by computing the overlap with monopole and contact interactions. Overall, both the TBRE and the empirical USDB had qualitatively similar results. The U.S. Department of Energy supported this investigation through contracts DE-FG02- 96ER40985 and DE-FC02-09ER41587, and through subcontract B576152 by Lawrence Liv- ermore National Laboratory under contract DE-AC52-07NA27344. [1] P.J. Brussard and P.W.M. Glaudemans, Shell-model applications in nuclear spectroscopy (North-Holland Publishing Company, Amsterdam, 1977). [2] B. A. Brown and B. H. Wildenthal, Annu. Rev. Nucl. Part. Sci. 38 , 29 (1988). [3] E. Caurier, G. Mart´ınez-Pinedo, F. Nowacki, A. Poves, and A. P. Zuker, Rev. Mod. Phys. 77 , 427 (2005). [4] P. Navr´ atil and W. E. Ormand, Phys. Rev. C 68 , 034305 (2003). [5] B.A. Brown and W.A. Richter, Phys. Rev. C 74 034315 (2006). [6] B.H. Wildenthal, Prog. Part. Nucl. Phys. 11 , 5 (1984). [7] A. Poves and A. Zuker: Phys. Rep. 70 , 235 (1981). [8] G. Mart´ınez-Pinedo, A. P. Zuker, A. Poves, and E. Caurier, Phys. Rev. C 55 187 (1997). [9] Y. Utsuno, T. Otsuka, T. Mizusaki, and M. Honma: Phys. Rev. C 60 , 054315 (1999). [10] M. Honma, T. Otsuka, B. A. Brown, and T. Mizusaki, Phys. Rev. C 69 , 034335 (2004). [11] T. Suzuki, S. Chiba, T. Yoshida, T. Kajino, and T. Otsuka Phys.Rev. C 74 , 034307 (2006). [12] G. F. Bertsch and C. W. Johnson, Phys. Rev. C 80 , 027302 (2009). 7