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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

A noncommutative algorithm for multiplying $3 \times 3$ matrices using 23 multiplications


Author: Julian D. Laderman
Journal: Bull. Amer. Math. Soc. 82 (1976), 126-128
MSC (1970): Primary 68A10, 65F30; Secondary 68A20, 65H10
MathSciNet review: 0395320
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  • 3. N. Gastinel, Sur le calcul des produits de matrices, Numer. Math. 17 (1971), 222–229 (French, with English summary). MR 0295550 (45 #4616)
  • 4. J. E. Hopcroft and L. R. Kerr, On minimizing the number of multiplications necessary for matrix multiplication, SIAM J. Appl. Math. 20 (1971), 30–36. MR 0274293 (43 #58)
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  • 6. I. Munro, Problems related to matrix multiplication, Proc. Courant Inst. Sympos. Computational Complexity, 1971, pp. 137-151.
  • 7. Volker Strassen, Gaussian elimination is not optimal, Numer. Math. 13 (1969), 354–356. MR 0248973 (40 #2223)
  • 8. S. Winograd, A new algorithm for inner product, IEEE Trans. Computers 17 (1968), 693-694.
  • 9. S. Winograd, On multiplication of 2×2 matrices, Linear Algebra and Appl. 4 (1971), 381–388. MR 0297115 (45 #6173)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9904-1976-13988-2
PII: S 0002-9904(1976)13988-2