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Karlin, Samuel; Pinkus, Allan

Oscillation properties of generalized characteristic polynomials for totally positive and positive definite matrices. (English) Zbl 0288.15013

Linear Algebra Appl. 8, 281-312 (1974).
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Cited in 6 Documents

MSC:

15A18 Eigenvalues, singular values, and eigenvectors
15B57 Hermitian, skew-Hermitian, and related matrices
15B48 Positive matrices and their generalizations; cones of matrices
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References:

[1] Crandall, H. G.; Rabinowitz, P. H., Bifurcation from simple eigenvalues, J. Functional Anal., 8, 321-340 (1971) · Zbl 0219.46015
[2] Gantmacher, F. R.; Krein, M. G., Oscillatory Matrices and Kernels and Small Vibrations of Mechanical Systems (1950), Moscow (Russian) · Zbl 0041.35502
[3] D.D. Joseph, Global Stability of Fluid Motions; D.D. Joseph, Global Stability of Fluid Motions
[4] Karlin, S., The existence of eigenvalues for integral operations, Trans. A.M.S., 113, 1-17 (1964) · Zbl 0178.46804
[5] Karlin, S., Oscillation properties of eigenvectors of strictly positive matrices, J. D’Anal. Math., 14, 247-266 (1965) · Zbl 0156.26603
[6] Karlin, S., Total Positivity, Vol. I (1968), Stanford Univ. Press: Stanford Univ. Press Stanford, Cal · Zbl 0219.47030
[7] S. Karlin, Total Positivity, Vol. II; S. Karlin, Total Positivity, Vol. II · Zbl 0219.47030
[8] Karlin, S.; McGregor, J., Coincidence probabilities, Pac. J. Math., 9, 1141-1164 (1959) · Zbl 0092.34503
[9] Karlin, S.; Studden, W. J., Tchebycheff Systems with Applications in Analysis and Statistics (1966), Interscience: Interscience New York · Zbl 0153.38902
[10] Lipow, P. R.; Schoenberg, I. J., Cardinal interpolation and spline functions. III. Cardinal Hermite interpolation, MRC Tech. Sum. Rep. #1113. MRC Tech. Sum. Rep. #1113, Linear Algebra and Appl., 6, 273-304 (June 1971) · Zbl 0246.41015
[11] Neumark, M., Linear Differential Operators (1967), Ungar: Ungar New York · Zbl 0219.34001
[12] Price, H. S., Monotone and oscillation matrices applied to finite difference approximations, Math. Comp., 22, 489-515 (1968) · Zbl 0162.47204
[13] Rabinowitz, P. H., A note on a nonlinear eigenvalue problem for a class of differential equations, J. Diff. Eq., 9, 536-548 (1971) · Zbl 0218.34027
[14] Schoenberg, I. J.; Sharma, A., Cardinal interpolation and spline functions. V. The \(B\)-splines for cardinal Hermite interpolation, MRC Tech. Sum. Rep. #1150. MRC Tech. Sum. Rep. #1150, Linear Algebra and Appl., 7, 1-42 (1973) · Zbl 0278.41010
[15] L.L. Schumaker, A Theory of Splines; L.L. Schumaker, A Theory of Splines · Zbl 0187.32802
[16] (Shisha, O., Inequalities I (1967), Academic: Academic New York)
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