Geodesic
Infinite extensions of Toeplitz matrices
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XVI, Tome 296 (2003), pp. 5-14

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A formula for the minimal rank of infinite Toeplitz extensions of a finite rectangular Toeplitz matrix is derived. 
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     author = {Yu. A. Alpin and S. N. Il'in},
     title = {Infinite extensions of {Toeplitz} matrices},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_296_a0/}
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Yu. A. Alpin; S. N. Il'in. Infinite extensions of Toeplitz matrices. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XVI, Tome 296 (2003), pp. 5-14. http://geodesic.mathdoc.fr/item/ZNSL_2003_296_a0/