# On the complexity of matrix product

@article{Raz2002OnTC, title={On the complexity of matrix product}, author={R. Raz}, journal={Electron. Colloquium Comput. Complex.}, year={2002} }

We prove a lower bound of &OHgr;(m2 log m) for the size of any arithmetic circuit for the product of two matrices, over the real or complex numbers, as long as the circuit doesn't use products with field elements of absolute value larger than 1 (where mxm is the size of each matrix). That is, our lower bound is super-linear in the number of inputs and is applied for circuits that use addition gates, product gates and products with field elements of absolute value up to 1.More generally, for any… CONTINUE READING

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#### References

SHOWING 1-2 OF 2 REFERENCES

Spectral methods for matrix rigidity with applications to size-depth tradeoffs and communication complexity

- Mathematics, Computer Science
- Proceedings of IEEE 36th Annual Foundations of Computer Science
- 1995

60 Highly Influential- PDF

A Spectral Approach to Lower Bounds with Applications to Geometric Searching

- Mathematics, Computer Science
- SIAM J. Comput.
- 1998

31 Highly Influential- PDF