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TU Berlin

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Ehemalige Mitarbeiter

Dr. Christian Ikenmeyer

Lupe

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Max-Planck-Institut für Informatik
Department 1: Algorithms and Complexity
Campus E1 4, Room 311D
66123 Saarbrücken
Germany
 
Persönliche Homepage
people.mpi-inf.mpg.de/~cikenmey/

Publikationen in der Arbeitsgruppe

Equations for lower bounds on border rank
Zitatschlüssel HIL-Equations-For-Lower-Bounds-On-Border-Rank
Autor Jonathan David Hauenstein and Christian Ikenmeyer and Joseph Montague Landsberg
Seiten 372–383
Jahr 2013
DOI 10.1080/10586458.2013.825892
Journal Experimental Mathematics
Jahrgang 22
Nummer 4
Zusammenfassung We present new methods for determining polynomials in the ideal of the variety of bilinear maps of border rank at most $r$. We apply these methods to several cases including the case $r = 6$ in the space of bilinear maps $\mathbb C^4 × \mathbb C^4 \to \mathbb C^4$. This space of bilinear maps includes the matrix multiplication operator $M_2$ for two by two matrices. We show these newly obtained polynomials do not vanish on the matrix multiplication operator $M_2$, which gives a new proof that the border rank of the multiplication of $2 × 2$ matrices is seven. Other examples are considered along with an explanation of how to implement the methods.
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