Произведение Кронекера: различия между версиями

: <math> (A \otimes B)^{-1} = A^{-1} \otimes B^{-1}. </math>

 

 

: <math> A \otimes B = (I \otimes B )(A \otimes I)</math>, где <math> I </math> - единичная матрица.

Произведение Трейси – Сингха определяется как<ref>{{cite journal |last=Tracy |first=D. S. |last2=Singh |first2=R. P. |year=1972 |title=A New Matrix Product and Its Applications in Matrix Differentiation |journal=Statistica Neerlandica |volume=26 |issue=4 |pages=143–157 |doi=10.1111/j.1467-9574.1972.tb00199.x }}</ref><ref>{{cite journal |last=Liu |first=S. |year=1999 |title=Matrix Results on the Khatri–Rao and Tracy–Singh Products |journal=Linear Algebra and Its Applications |volume=289 |issue=1–3 |pages=267–277 |doi=10.1016/S0024-3795(98)10209-4 }}</ref>

 

 

Например:

 

:<math>\begin{align}

= \left[\begin{array} {c | c}

\hline

\end{array}\right]

={} &\left[\begin{array} {c | c | c | c}