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Smith, P. W.; Wolkowicz, Henry

Dimensionality of biinfinite systems. (English) Zbl 0527.15004

Linear Algebra Appl. 57, 115-130 (1984).
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MSC:

15A18 Eigenvalues, singular values, and eigenvectors
15B57 Hermitian, skew-Hermitian, and related matrices
15A09 Theory of matrix inversion and generalized inverses
41A05 Interpolation in approximation theory
15A30 Algebraic systems of matrices

Keywords:

coefficient of interpolation of compactly supported real functions; biinfinite sequence of interpolation points; kernel of the biinfinite block Toeplitz matrix; dimension; maximal solvable subspace; Kronecker canonical form; matrix pencil; restricted generalized inverses
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References:

[1] Ben-Israel, A.; Greville, G. W.E., Generalized Inverses: Theory and Applications (1974), Wiley-Interscience · Zbl 0305.15001
[2] Cavaretta, A. S.; Dahmen, W. A.; Micchelli, C. A.; Smith, P. W., On the solvability of certain systems of linear difference equations, SIAM J. Math. Anal., 12, 833-841 (1981) · Zbl 0482.15011
[3] Van Dooren, Paul M., The generalized eigenstructure problem in linear system theory, IEEE Trans. Automatic Control, AC-26, 111-129 (1981) · Zbl 0462.93013
[4] Van Dooren, P., The computation of Kronecker’s canonical form of a singular pencil, Linear Algebra Appl., 27, 103-141 (1979) · Zbl 0416.65026
[5] Gantmacher, F. R., Theory of Matrices, Vol. I,II (1959), Chelsea: Chelsea New York · Zbl 0085.01001
[6] Golub, G. H.; Wilkinson, J. H., Ill-conditioned eigensystems and the computation of the Jordan canonical form, SIAM Rev., 18, 579-619 (1976) · Zbl 0341.65027
[7] S.L. Lee, C.A. Micchelli, A. Sharma, and P.W. Smith, Some properties of periodic \(B\)Proc. Edinburgh Math. Soc.; S.L. Lee, C.A. Micchelli, A. Sharma, and P.W. Smith, Some properties of periodic \(B\)Proc. Edinburgh Math. Soc. · Zbl 0537.41005
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