کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4603352 | 1631174 | 2007 | 16 صفحه PDF | دانلود رایگان |

The following inverse eigenvalue problem was introduced and discussed in [J. Peng, X.Y. Hu, L. Zhang, Two inverse eigenvalue problems for a special kind of matrices, Linear Algebra Appl. 416 (2006) 336–347]: to construct a real symmetric bordered diagonal matrix A from the minimal and maximal eigenvalues of all its leading principal submatrices. However, the given formulae in [4, Theorem 1] to compute the matrix A may lead us to a matrix, which does not satisfy the requirements of the problem. In this paper, we rediscuss the problem to give a sufficient condition for the existence of such a matrix and necessary and sufficient conditions for the existence of a nonnegative such a matrix. Results are constructive and generate an algorithmic procedure to construct the matrices.
Journal: Linear Algebra and its Applications - Volume 427, Issues 2–3, 1 December 2007, Pages 256-271