Strassen algorithm

Theorem for the Strassen algorithm

Computing the matrix product [math]\displaystyle{ AA^T }[/math] shortens the original runtime [math]\displaystyle{ T(n) = \mathcal{O}(n^{(_2 7)}) }[/math] of the Strassen algorithm roughly by [math]\displaystyle{ \tilde{3} }[/math] for sufficiently big [math]\displaystyle{ n := 2^k, k \in \mathbb{N}^* }[/math] and the matrix [math]\displaystyle{ A \in \mathbb{C}^{n \times n} }[/math] due to the geometric series and

[math]\displaystyle{ A := \begin{pmatrix} A_{11} & A_{12} \\ A_{21} & A_{22} \end{pmatrix} }[/math] as well as [math]\displaystyle{ AA^T = \begin{pmatrix} A_{11}A_{11}^T+A_{12}A_{12}^T & A_{11}A_{21}^T+A_{12}A_{22}^T \\ A_{21}A_{11}^T+A_{22}A_{12}^T & A_{21}A_{21}^T+A_{22}A_{22}^T \end{pmatrix}.\square }[/math]

See also

List of mathematical symbols