𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On singular values of partially prescribed matrices

✍ Scribed by Pedro M.Q. Aguiar; Marko Stošić; João Xavier

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
150 KB
Volume
429
Category
Article
ISSN
0024-3795

No coin nor oath required. For personal study only.

✦ Synopsis

In this paper we study singular values of a matrix whose one entry varies while all other entries are prescribed. In particular, we find the possible pth singular value of such a matrix, and we define explicitly the unknown entry such that the completed matrix has the minimal possible pth singular value. This in turn determines possible pth singular value of a matrix under rank one perturbation. Moreover, we determine the possible value of pth singular value of a partially prescribed matrix whose set of unknown entries has a form of a Young diagram. In particular, we give a fast algorithm for defining the completion that minimizes the pth singular value of such matrix.

📜 SIMILAR VOLUMES

Nonnegative matrices with prescribed ext
Nonnegative matrices with prescribed extremal singular values
✍ Emedin Montaño; Mario Salas; Ricardo L. Soto 📂 Article 📅 2008 🏛 Elsevier Science 🌐 English ⚖ 295 KB

We consider the problem of constructing nonnegative matrices with prescribed extremal singular values. In particular, given 2n -1 real numbers σ ( j) 1 and σ ( j) j , j = 1, . . . , n, we construct an n × n nonnegative bidiagonal matrix B and an n × n nonnegative semi-bordered diagonal matrix C, suc

SINGULAR VALUES OF CUMULANT MATRICES
SINGULAR VALUES OF CUMULANT MATRICES
✍ M. Rokni; B.S. Berger; I. Minis 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 159 KB

The identification of cutting states, associated with the orthogonal cutting of stiff cylinders, was realized in reference [1] through an analysis of the singular values of an unsymmetric Toeplitz matrix, R, of third order cumulants, r(i, j), of acceleration measurements. The ratio of the two domina