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I remember reading somewhere that if matrix multiplication can be done in $O(n^\omega)$ time then determinants can be computed in $O(n^\omega)$ time. I am unable to find the reduction and would it be possible for someone to share the reference?

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  • $\begingroup$ Try the book Algebraic Complexity Theory by Burgisser et al. $\endgroup$ – Yuval Filmus Feb 14 '16 at 6:16
  • $\begingroup$ @YuvalFilmus I am also looking for 1 more piece of info. Group algebras and Matrix mult are related and matrix mult and determinants are related and so is there a relation between convolution in group algebras and determinant (and also permanent)? $\endgroup$ – user39969 Feb 14 '16 at 19:39

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