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The algorithmic complexity of linear algebras

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Algorithms in Modern Mathematics and Computer Science

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 122))

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Abstract

The complexity L(A) of a finite dimensional associative algebra A is the number of non-scalar multiplications/divisions of an optimal algorithm to compute the product of two elements of the algebra. We show

$$L(A) \geqslant 2 \cdot dimA - t,$$

where t is the number of maximal two-sided ideals of A.

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Authors

Editor information

Andrei P. Ershov Donald E. Knuth

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Dedicated to Al-Khowarizmi

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© 1981 Springer-Verlag Berlin Heidelberg

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Alder, A., Strassen, V. (1981). The algorithmic complexity of linear algebras. In: Ershov, A.P., Knuth, D.E. (eds) Algorithms in Modern Mathematics and Computer Science. Lecture Notes in Computer Science, vol 122. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-11157-3_34

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  • DOI: https://doi.org/10.1007/3-540-11157-3_34

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11157-3

  • Online ISBN: 978-3-540-38621-6

  • eBook Packages: Springer Book Archive

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