Part of the Lecture Notes in Computer Science book series (LNCS, volume 122)
The algorithmic complexity of linear algebras
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
where t is the number of maximal two-sided ideals of A.
$$L(A) \geqslant 2 \cdot dimA - t,$$
KeywordsMatrix Multiplication Left Ideal Division Algebra Linear Independence Semisimple Algebra
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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