Table 3.

Matrix operations complexity sum-up.

Operation	$\mathit{T}\mathbf{(}\mathbf{.}\mathbf{)}$	$\mathcal{O}\mathbf{(}\mathbf{.}\mathbf{)}$
Matrix multiplication	$2\times n\times m\times p$	$2\times n\times m\times p$
Adding two vectors of size n	n	n
Adding two matrices of size $(n,m)$	$n\times m$	$n\times m$
Transpose a matrix	0	0
Invert a matrix	$4\times n^3+2\times n^2$	$4\times n^3$
Mean vector of a matrix	$n\times (m+1)$	$n\times m$
Mean value of a vector	$n+1$	n
Covariance de deux matrices	$2\times n\times m\times p$	$2\times n\times m\times p$