master-degree-notes/Foundation of data science/slides/Untitled.md

$$fm,n]+[m^{\prime},n^{\prime}=f\left\lbrack m+m^{\prime},n+n^{\prime}\right\rbrack=f\left\lbrack m,n\right\rbrack+f\left\lbrack m^{\prime},n^{\prime}\right\rbrack

\sum_{k,l}{I[(m+m')-k,(n+n')-l]g[k,l]}=\sum_{k,l}{I[m-k,n-l]g[k,l]}+\sum_{k,l}{I[m'-k,n'-l]g[k,l]}

\sum_{k,l}{I[(m+m')-k,(n+n')-l]g[k,l]}=\sum_{k,l}{I[m-k,n-l]g[k,l] + I[m'-k,n'-l]g[k,l]}

\sum_{k,l}{I[(m+m')-k,(n+n')-l]g[k,l]}=\sum_{k,l}{(I[m-k,n-l] + I[m'-k,n'-l])g[k,l]}

\sum_{k,l}{I[(m+m')-k,(n+n')-l]g[k,l]}=\sum_{k,l}{I[(m+m')-k,(n+n')-l]g[k,l]}