We show, for the input vectors (a0β,a1β,...,anβ1β) and (b0β,b1β,...,bnβ1β), where aiβ's and bjβ's are real numbers, after \~{O}(n)
time preprocessing for each of them, the vector multiplication (a0β,a1β,...,anβ1β)(b0β,b1β,...,bnβ1β)T can be computed in \~{O}(1) time. This
enables the matrix multiplication of two nΓn matrices to be computed in
\~{O}(n2) time.Comment: Version 11 and Version 12 section 2 laid the foundation of this
algorithm but has a problem unresolved. This version corrects the problem in
Version 11 and Section 2 of Version 1