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Matrices, moments, and rational quadrature

✍ Scribed by G. López Lagomasino; L. Reichel; L. Wunderlich

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

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📜 SIMILAR VOLUMES

The moment and Gram matrices, distinct e
The moment and Gram matrices, distinct eigenvalues and zeroes, and rational criteria for diagonalizability
✍ Roger A. Horn; Alexey K. Lopatin 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 94 KB

The moment matrix of order m associated with the n-by-n complex matrix A is K m ≡ trA i+j -2 m i,j =1 . We show that d ≡ rank K n is the number of distinct eigenvalues of A, d = max {m = 1, . . . , n: K m is nonsingular}, and there is a unique (d + 1)-vector a ≡ a i-1 d+1 i=1 such that K d+1 a = 0