Geodesic
On bilinear complexity of multiplication of $5\times2$ matrix by $2\times2$ matrix
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 156 (2014) no. 3, pp. 19-29

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In this paper we study bilinear complexity (i.e. the minimum number of multiplications without using commutativity of the elements) for the problem of multiplication of matrices of small size. We show that the bilinear complexity for the problem of multiplication of a $5\times2$ matrix by a $2\times~2$ matrix is at least 17 for any field.
Mots-clés : matrix multiplication
Keywords: algorithm, complexity, bilinear complexity. 
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     author = {V. B. Alekseev},
     title = {On bilinear complexity of multiplication of $5\times2$ matrix by $2\times2$ matrix},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {19--29},
     publisher = {mathdoc},
     volume = {156},
     number = {3},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2014_156_3_a2/}
}
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V. B. Alekseev. On bilinear complexity of multiplication of $5\times2$ matrix by $2\times2$ matrix. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 156 (2014) no. 3, pp. 19-29. http://geodesic.mathdoc.fr/item/UZKU_2014_156_3_a2/