Inverse Problems Of Several Special Matrices Generalized Eigenvalue And Mixed Spectrum Data

Inverse problems of matrices have been widely used in control theory, economic field, vibration theory and civil construction engineering. We will systematically study some generalized inverse eigenvalue problems of matrices in the second chapter of this M.S. thesis and mainly discuss the following problems:What we mainly discussed in the second chapter as follows:(1) S1,S2 are sets of symmetric orth-symmetric matrices;(2) S1,S2 are sets of bisymmetric matrices;(3) S1,S2 are sets of anti-symmetric orth-anti-symmetric matrices;(4) S1,S2 are sets of bi-anti-symmetric matrices;(5) S1 is the set of symmetric orth-symmetric matrices, S2 is the set of anti-symmetric orth-anti-symmetric matrices;(6) S1 is the set of bisymmetric matrices, S2 is the set of bi-anti-symmetric matrices;(7) S1 is the set of anti-symmetric orth-anti-symmetric matrices, S2 is the set of symmetric orth-symmetric matrices;(8) S1 is the set of bi-anti-symmetric matrices, S2 is the set of bisymmetricmatrices;On the base of studying the basic properties of the matrices, the expression of solutions and some numerical examples are presented.We study inverse problem of mixed Spectrum Data in the third chapter of thisM.S. thesis, i.e. inverse problem of eigenvalue and singular value, many fundamental topics in linear algebra and important applications in practice are best understood when formulated in terms of the singular value decomposition.