Relevant bibliographies by topics / Positive-definite matrices

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Academic literature on the topic 'Positive-definite matrices'

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Published: 4 June 2021
Last updated: 14 February 2022

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Journal articles on the topic "Positive-definite matrices"

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Töllis, Theodore. "On means of positive definite matrices." Czechoslovak Mathematical Journal 37, no. 4 (1987): 628–41. http://dx.doi.org/10.21136/cmj.1987.102190.

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Mostajeran, Cyrus, and Rodolphe Sepulchre. "Ordering positive definite matrices." Information Geometry 1, no. 2 (May 15, 2018): 287–313. http://dx.doi.org/10.1007/s41884-018-0003-7.

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Rosen, Lon. "Positive Powers of Positive Positive Definite Matrices." Canadian Journal of Mathematics 48, no. 1 (February 1, 1996): 196–209. http://dx.doi.org/10.4153/cjm-1996-009-9.

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AbstractLet C be an n x n positive definite matrix. If C ≥ 0 in the sense that Cij ≥ 0 and if p > n — 2, then Cp ≥ 0. This implies the following "positive minorant property" for the norms ‖A‖p = [tr(A*A)p/2]1/P. Let 2 < p ≠ 4, 6, … . Then 0 ≤ A ≤ B => ‖A‖p ≥ ‖B‖P if and only if n < p/2 + 1.
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Fiedler, Miroslav, and Vlastimil Pták. "A new positive definite geometric mean of two positive definite matrices." Linear Algebra and its Applications 251 (January 1997): 1–20. http://dx.doi.org/10.1016/0024-3795(95)00540-4.

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Markham, Thomas L. "Oppenheim's Inequality for Positive Definite Matrices." American Mathematical Monthly 93, no. 8 (October 1986): 642. http://dx.doi.org/10.2307/2322329.

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Gilbert, George T. "Positive Definite Matrices and Sylvester's Criterion." American Mathematical Monthly 98, no. 1 (January 1991): 44. http://dx.doi.org/10.2307/2324036.

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Cui, Jianlian, Chi-Kwong Li, and Nung-Sing Sze. "Products of positive semi-definite matrices." Linear Algebra and its Applications 528 (September 2017): 17–24. http://dx.doi.org/10.1016/j.laa.2015.09.045.

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Ichi Fujii, Jun, and Masatoshi Fujii. "Kolmogorov's complexity for positive definite matrices." Linear Algebra and its Applications 341, no. 1-3 (January 2002): 171–80. http://dx.doi.org/10.1016/s0024-3795(01)00354-8.

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Markham, Thomas L. "Oppenheim's Inequality for Positive Definite Matrices." American Mathematical Monthly 93, no. 8 (October 1986): 642–44. http://dx.doi.org/10.1080/00029890.1986.11971910.

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Gilbert, George T. "Positive Definite Matrices and Sylvester's Criterion." American Mathematical Monthly 98, no. 1 (January 1991): 44–46. http://dx.doi.org/10.1080/00029890.1991.11995702.

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Dissertations / Theses on the topic "Positive-definite matrices"

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Heyfron, Peter. "Positive functions defined on Hermitian positive semi-definite matrices." Thesis, Imperial College London, 1990. http://hdl.handle.net/10044/1/46339.

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Ho, Man-Kiu, and 何文翹. "Iterative methods for non-hermitian positive semi-definite systems." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2004. http://hub.hku.hk/bib/B30289403.

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Cavers, Ian Alfred. "Tiebreaking the minimum degree algorithm for ordering sparse symmetric positive definite matrices." Thesis, University of British Columbia, 1987. http://hdl.handle.net/2429/27855.

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The minimum degree algorithm is known as an effective scheme for identifying a fill reduced ordering for symmetric, positive definite, sparse linear systems, to be solved using a Cholesky factorization. Although the original algorithm has been enhanced to improve the efficiency of its implementation, ties between minimum degree elimination candidates are still arbitrarily broken. For many systems, the fill levels of orderings produced by the minimum degree algorithm are very sensitive to the precise manner in which these ties are resolved. This thesis introduces several tiebreaking enhancements of the minimum degree algorithm. Emphasis is placed upon a tiebreaking strategy based upon the deficiency of minium degree elimination candidates, and which can consistently identify low fill orderings for a wide spectrum of test problems. All tiebreaking strategies are fully integrated into implementations of the minimum degree algorithm based upon a quotient graph model, including indistinguishable sets represented by uneliminated supernodes. The resulting programs are tested on a wide variety of sparse systems in order to investigate the performance of the algorithm enhanced by the tiebreaking strategies and the quality of the orderings they produce.
Science, Faculty of
Computer Science, Department of
Graduate
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Birk, Sebastian [Verfasser]. "Deflated Shifted Block Krylov Subspace Methods for Hermitian Positive Definite Matrices / Sebastian Birk." Wuppertal : Universitätsbibliothek Wuppertal, 2015. http://d-nb.info/1073127559/34.

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Woodgate, K. G. "Optimization over positive semi-definite symmetric matrices with application to Quasi-Newton algorithms." Thesis, Imperial College London, 1987. http://hdl.handle.net/10044/1/46914.

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Tsai, Wenyu Julie. "Neural computation of the eigenvectors of a symmetric positive definite matrix." CSUSB ScholarWorks, 1996. https://scholarworks.lib.csusb.edu/etd-project/1242.

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Nader, Rafic. "A study concerning the positive semi-definite property for similarity matrices and for doubly stochastic matrices with some applications." Thesis, Normandie, 2019. http://www.theses.fr/2019NORMC210.

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La théorie des matrices s'est développée rapidement au cours des dernières décennies en raison de son large éventail d'applications et de ses nombreux liens avec différents domaines des mathématiques, de l'économie, de l'apprentissage automatique et du traitement du signal. Cette thèse concerne trois axes principaux liés à deux objets d'étude fondamentaux de la théorie des matrices et apparaissant naturellement dans de nombreuses applications, à savoir les matrices semi-définies positives et les matrices doublement stochastiques.Un concept qui découle naturellement du domaine de l'apprentissage automatique et qui est lié à la propriété semi-définie positive est celui des matrices de similarité. En fait, les matrices de similarité qui sont semi-définies positives revêtent une importance particulière en raison de leur capacité à définir des distances métriques. Cette thèse explorera la propriété semi-définie positive pour une liste de matrices de similarité trouvées dans la littérature. De plus, nous présentons de nouveaux résultats concernant les propriétés définie positive et semi-définie trois-positive de certains matrices de similarité. Une discussion détaillée des nombreuses applications de tous ces propriétés dans divers domaines est également établie.D'autre part, un problème récent de l'analyse matricielle implique l'étude des racines des matrices stochastiques, ce qui s'avère important dans les modèles de chaîne de Markov en finance. Nous étendons l'analyse de ce problème aux matrices doublement stochastiques semi-définies positives. Nous montrons d'abord certaines propriétés géométriques de l'ensemble de toutes les matrices semi-définies positives doublement stochastiques d'ordre n ayant la p-ième racine doublement stochastique pour un entier donné p . En utilisant la théorie des M-matrices et le problème inverse des valeurs propres des matrices symétriques doublement stochastiques (SDIEP), nous présentons également quelques méthodes pour trouver des classes de matrices semi-définies positives doublement stochastiques ayant des p-ièmes racines doublement stochastiques pour tout entier p.Dans le contexte du SDIEP, qui est le problème de caractériser ces listes de nombres réels qui puissent constituer le spectre d’une matrice symétrique doublement stochastique, nous présentons quelques nouveaux résultats le long de cette ligne. En particulier, nous proposons d’utiliser une méthode récursive de construction de matrices doublement stochastiques afin d'obtenir de nouvelles conditions suffisantes indépendantes pour SDIEP. Enfin, nous concentrons notre attention sur les spectres normalisés de Suleimanova, qui constituent un cas particulier des spectres introduits par Suleimanova. En particulier, nous prouvons que de tels spectres ne sont pas toujours réalisables et nous construisons trois familles de conditions suffisantes qui affinent les conditions suffisantes précédemment connues pour SDIEP dans le cas particulier des spectres normalisés de Suleimanova
Matrix theory has shown its importance by its wide range of applications in different fields such as statistics, machine learning, economics and signal processing. This thesis concerns three main axis related to two fundamental objects of study in matrix theory and that arise naturally in many applications, that are positive semi-definite matrices and doubly stochastic matrices.One concept which stems naturally from machine learning area and is related to the positive semi-definite property, is the one of similarity matrices. In fact, similarity matrices that are positive semi-definite are of particular importance because of their ability to define metric distances. This thesis will explore the latter desirable structure for a list of similarity matrices found in the literature. Moreover, we present new results concerning the strictly positive definite and the three positive semi-definite properties of particular similarity matrices. A detailed discussion of the many applications of all these properties in various fields is also established.On the other hand, an interesting research field in matrix analysis involves the study of roots of stochastic matrices which is important in Markov chain models in finance and healthcare. We extend the analysis of this problem to positive semi-definite doubly stochastic matrices.Our contributions include some geometrical properties of the set of all positive semi-definite doubly stochastic matrices of order n with nonnegative pth roots for a given integer p. We also present methods for finding classes of positive semi-definite doubly stochastic matrices that have doubly stochastic pth roots for all p, by making use of the theory of M-Matrices and the symmetric doubly stochastic inverse eigenvalue problem (SDIEP), which is also of independent interest.In the context of the SDIEP, which is the problem of characterising those lists of real numbers which are realisable as the spectrum of some symmetric doubly stochastic matrix, we present some new results along this line. In particular, we propose to use a recursive method on constructing doubly stochastic matrices from smaller size matrices with known spectra to obtain new independent sufficient conditions for SDIEP. Finally, we focus our attention on the realizability by a symmetric doubly stochastic matrix of normalised Suleimanova spectra which is a normalized variant of the spectra introduced by Suleimanova. In particular, we prove that such spectra is not always realizable for odd orders and we construct three families of sufficient conditions that make a refinement for previously known sufficient conditions for SDIEP in the particular case of normalized Suleimanova spectra
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陳志輝 and Chi-fai Alan Bryan Chan. "Some aspects of generalized numerical ranges and numerical radii associated with positive semi-definite functions." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1993. http://hub.hku.hk/bib/B31232954.

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Chan, Chi-fai Alan Bryan. "Some aspects of generalized numerical ranges and numerical radii associated with positive semi-definite functions /." [Hong Kong : University of Hong Kong], 1993. http://sunzi.lib.hku.hk/hkuto/record.jsp?B13525256.

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Bajracharya, Neeraj. "Level Curves of the Angle Function of a Positive Definite Symmetric Matrix." Thesis, University of North Texas, 2009. https://digital.library.unt.edu/ark:/67531/metadc28376/.

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Given a real N by N matrix A, write p(A) for the maximum angle by which A rotates any unit vector. Suppose that A and B are positive definite symmetric (PDS) N by N matrices. Then their Jordan product {A, B} := AB + BA is also symmetric, but not necessarily positive definite. If p(A) + p(B) is obtuse, then there exists a special orthogonal matrix S such that {A, SBS^(-1)} is indefinite. Of course, if A and B commute, then {A, B} is positive definite. Our work grows from the following question: if A and B are commuting positive definite symmetric matrices such that p(A) + p(B) is obtuse, what is the minimal p(S) such that {A, SBS^(-1)} indefinite? In this dissertation we will describe the level curves of the angle function mapping a unit vector x to the angle between x and Ax for a 3 by 3 PDS matrix A, and discuss their interaction with those of a second such matrix.
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Books on the topic "Positive-definite matrices"

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Positive definite matrices. Princeton, N.J: Princeton University Press, 2007.

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R, Johnson Charles, and Loewy Raphael 1943-, eds. The real positive definite completion problem: Cycle completability. Providence, R.I: American Mathematical Society, 1996.

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Fischer, Bernd. On adaptive weighted polynomial preconditioning for Hermitian positive definite matrices. [Moffett Field, Calif.]: Research Institute for Advanced Computer Science, NASA Ames Research Center, 1992.

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Bhatia, Rajendra. Positive Definite Matrices. Princeton University Press, 2015.

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Bhatia, Rajendra. Positive definite matrices. [s.l.] : Hindustan book Agency : 2007, 2007.

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Bhatia, Rajendra. Positive Definite Matrices. Princeton University Press, 2009.

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Bhatia, Rajendra. Positive Definite Matrices. Princeton University Press, 2009.

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Bhatia, Rajendra. Positive Definite Matrices (Princeton Series in Applied Mathematics). Princeton University Press, 2006.

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Schomerus, Henning. Random matrix approaches to open quantum systems. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797319.003.0010.

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Over the past decades, a great body of theoretical and mathematical work has been devoted to random-matrix descriptions of open quantum systems. This chapter reviews the physical origins and mathematical structures of the underlying models, and collects key predictions which give insight into the typical system behaviour. In particular, the aim is to give an idea how the different features are interlinked. The chapter mainly focuses on elastic scattering but also includes a short detour to interacting systems, which are motivated by the overarching question of ergodicity. The first sections introduce general notions from random matrix theory, such as the 10 universality classes and ensembles of Hermitian, unitary, positive-definite, and non-Hermitian matrices. The following sections then review microscopic scattering models that form the basis for statistical descriptions, and consider signatures of random scattering in decay, dynamics, and transport. The last section touches on Anderson localization and localization in interacting systems.
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Book chapters on the topic "Positive-definite matrices"

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Foias, Ciprian, and Arthur E. Frazho. "Positive Definite Block Matrices." In The Commutant Lifting Approach to Interpolation Problems, 547–86. Basel: Birkhäuser Basel, 1990. http://dx.doi.org/10.1007/978-3-0348-7712-1_16.

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Conley, Charles H. "VII.2 Positive Definite Matrices." In James Serrin. Selected Papers, 839–62. Basel: Springer Basel, 2014. http://dx.doi.org/10.1007/978-3-0348-0847-7_18.

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Yuan, Xinru, Wen Huang, Pierre-Antoine Absil, and Kyle A. Gallivan. "Averaging Symmetric Positive-Definite Matrices." In Handbook of Variational Methods for Nonlinear Geometric Data, 555–75. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-31351-7_20.

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Bapat, R. B. "Eigenvalues and Positive Definite Matrices." In Linear Algebra and Linear Models, 21–29. London: Springer London, 2012. http://dx.doi.org/10.1007/978-1-4471-2739-0_3.

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Fiedler, Miroslav. "Symmetric Matrices. Positive Definite and Semidefinite Matrices." In Special matrices and their applications in numerical mathematics, 39–64. Dordrecht: Springer Netherlands, 1986. http://dx.doi.org/10.1007/978-94-009-4335-3_2.

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Lyche, Tom. "LDL* Factorization and Positive Definite Matrices." In Numerical Linear Algebra and Matrix Factorizations, 83–98. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-36468-7_4.

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Dym, Harry. "Triangular factorization and positive definite matrices." In Graduate Studies in Mathematics, 251–90. Providence, Rhode Island: American Mathematical Society, 2013. http://dx.doi.org/10.1090/gsm/078/12.

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Lyche, Tom, Georg Muntingh, and Øyvind Ryan. "LDL* Factorization and Positive Definite Matrices." In Texts in Computational Science and Engineering, 61–65. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-59789-4_4.

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Muñoz, Alberto, and Isaac Martí n. de Diego. "From Indefinite to Positive Semi-Definite Matrices." In Lecture Notes in Computer Science, 764–72. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11815921_84.

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Cherian, Anoop, and Suvrit Sra. "Riemannian Sparse Coding for Positive Definite Matrices." In Computer Vision – ECCV 2014, 299–314. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-10578-9_20.

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Conference papers on the topic "Positive-definite matrices"

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Aftab, Khurrum, and Richard Hartley. "Lq Averaging for Symmetric Positive-Definite Matrices." In 2013 International Conference on Digital Image Computing: Techniques and Applications (DICTA). IEEE, 2013. http://dx.doi.org/10.1109/dicta.2013.6691505.

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Recasens, Jordi. "Characterizing Positive Definite Matrices with t-norms." In Proceedings of the 2019 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology (EUSFLAT 2019). Paris, France: Atlantis Press, 2019. http://dx.doi.org/10.2991/eusflat-19.2019.14.

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Jahromi, Mehdi, Kon Wong, and Aleksandar Jeremic. "Estimating Positive Definite Matrices using Frechet Mean." In International Conference on Bio-inspired Systems and Signal Processing. SCITEPRESS - Science and and Technology Publications, 2015. http://dx.doi.org/10.5220/0005277902950299.

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Stanitsas, Panagiotis, Anoop Cherian, Vassilios Morellas, and Nikolaos Papanikolopoulos. "Clustering Positive Definite Matrices by Learning Information Divergences." In 2017 IEEE International Conference on Computer Vision Workshop (ICCVW). IEEE, 2017. http://dx.doi.org/10.1109/iccvw.2017.155.

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Cherian, A., P. Stanitsas, M. Harandi, V. Morellas, and N. Papanikolopoulos. "Learning Discriminative αβ-Divergences for Positive Definite Matrices." In 2017 IEEE International Conference on Computer Vision (ICCV). IEEE, 2017. http://dx.doi.org/10.1109/iccv.2017.458.

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Faraki, Masoud, Mehrtash T. Harandi, and Fatih Porikli. "Image set classification by symmetric positive semi-definite matrices." In 2016 IEEE Winter Conference on Applications of Computer Vision (WACV). IEEE, 2016. http://dx.doi.org/10.1109/wacv.2016.7477621.

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Todros, Koby, and Joseph Tabrikian. "Fast Approximate Joint Diagonalization of Positive Definite Hermitian Matrices." In 2007 IEEE International Conference on Acoustics, Speech, and Signal Processing. IEEE, 2007. http://dx.doi.org/10.1109/icassp.2007.367101.

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Starek, Ladislav, Daniel J. Inman, and Deborah F. Pilkev. "A Symmetric Positive Definite Inverse Vibration Problem With Underdamped Modes." In ASME 1995 Design Engineering Technical Conferences collocated with the ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium. American Society of Mechanical Engineers, 1995. http://dx.doi.org/10.1115/detc1995-0682.

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Abstract This manuscript considers a symmetric positive definite inverse eigenvalue problem for linear vibrating systems described by a vector differential equation with constant coefficient matrices. The inverse problem of interest here is that of determining real symmetric, positive definite coefficient matrices assumed to represent the mass normalized velocity and position coefficient matrices, given a set of specified eigenvalues and eigenvectors. The approach presented here gives an alternative solution to a symmetric inverse vibration problem presented by Starek and Inman (1992) and extends these results to include the definiteness of the coefficient matrices. The new results give conditions which allow the construction of mass normalized damping and stiffness matrices based on given eigenvalues and eigenvectors for the case that each mode of the system is underdamped. The result provides an algorithm for determining a non-proportional damped system which will have symmetric positive definite coefficient matrices.
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Boumal, Nicolas, and P. A. Absil. "Discrete regression methods on the cone of positive-definite matrices." In ICASSP 2011 - 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2011. http://dx.doi.org/10.1109/icassp.2011.5947287.

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Wang, Xiyuan, Kun Wang, Zhongshan Zhang, and Keping Long. "1-Bit compressed sensing of positive semi-definite matrices via rank-1 measurement matrices." In 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2016. http://dx.doi.org/10.1109/icassp.2016.7472551.

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