A = \begin{bmatrix}
a_{0,0} & a_{0,1} &&&&&& a_{0,7}\\
a_{1,0} & a_{1,1} &&&&& a_{1,6}\\
&& a_{2,2} & a_{2,3} && a_{2,5} \\
&& a_{3,2} & a_{3,3} & a_{3,4}\\
&&& a_{4,3} & a_{4,4} & a_{4,5}\\
&& a_{5,2} && a_{5,5} & a_{5,5} & \\
& a_{6,1}&&&&& a_{6,6} & a_{6,7} \\
a_{7,0} &&&&&& a_{7,6} & a_{7,7}\\
\end{bmatrix}
C = \begin{bmatrix}
c_{0}\\
c_{1}\\
c_{2}\\
c_{3}\\
c_{4}\\
c_{5}\\
c_{6}\\
c_{7}\\
\end{bmatrix}
A = \begin{bmatrix}
a_{0,0} & a_{0,1} & a_{0,15}\\
a_{1,0} & a_{1,1} & a_{1,14}\\
a_{2,2} & a_{2,3} & a_{2,13} \\
a_{3,2} & a_{3,3} & a_{3,12}\\
a_{4,4} & a_{4,5} & a_{4,11}\\
a_{5,4} & a_{5,5} & a_{5,10}\\
a_{6,6} & a_{6,7} & a_{6,9}\\
a_{7,6} & a_{7,7} & a_{7,8}\\
a_{8,7} & a_{8,8} & a_{8,9}\\
a_{9,6} & a_{9,8} & a_{9.9} \\
a_{10,5} & a_{10,10} & a_{10,11} \\
a_{11,4} & a_{11,10} & a_{11,11} \\
a_{12,3} & a_{12,12} & a_{12,13} \\
a_{13,2} & a_{13,12} & a_{13,13} \\
a_{14,1} & a_{14,14} & a_{14,15}\\
a_{15,0} & a_{15,14} & a_{15,15} \\
\end{bmatrix}
C = \begin{bmatrix}
c_{0}\\
c_{1}\\
c_{2}\\
c_{3}\\
c_{4}\\
c_{5}\\
c_{6}\\
c_{7}\\
c_{8}\\
c_{9}\\
c_{10}\\
c_{11}\\
c_{12}\\
c_{13}\\
c_{14}\\
c_{15}\\
\end{bmatrix}
\(A = \left[ \begin{smallmatrix}a_{0,0} \ & a_{0,1} & & & & & & & & & & & & & & a_{0,15}\\a_{1,0} & a_{1,1} & & & & & & & & & & & & & a_{1,14}\\& & a_{2,2} & a_{2,3} & & & & & & & & & & a_{2,13} \\& & a_{3,2} & a_{3,3} & & & & & & & & & a_{3,12}\\& & & & a_{4,4} & a_{4,5} & & & & & & a_{4,11}\\& & & & a_{5,4} & a_{5,5} & & & & & a_{5,10}\\& & & & & & a_{6,6} & a_{6,7} & & a_{6,9}\\& & & & & & a_{7,6} & a_{7,7} & a_{7,8}\\& & & & & & & a_{8,7}& a_{8,8} & a_{8,9}\\& & & & & & a_{9,6}& & a_{9,8} & a_{9.9} &\\& & & & & a_{10,5} & & & & & a_{10,10} & a_{10,11} \\& & & & a_{11,4} & & & & & & a_{11,10} & a_{11,11} & \\& & & a_{12,3} & & & & & & & & & a_{12,12} & a_{12,13} \\& & a_{13,2} & & & & & & & & & & a_{13,12} & a_{13,13} &\\& a_{14,1}& & & & & & & & & & & & & a_{14,14} & a_{14,15}\\a_{15,0}& & & & & & & & & & & & & & a_{15,14} & a_{15,15} \\\end{smallmatrix} \right]\)
\(C = \left[ \begin{smallmatrix} c_{0}\\ c_{1}\\ c_{2}\\ c_{3}\\ c_{4}\\ c_{5}\\ c_{6}\\ c_{7}\\ c_{8}\\ c_{9}\\ c_{10}\\ c_{11}\\ c_{12}\\ c_{13}\\ c_{14}\\ c_{15}\\ \end{smallmatrix}\right] \)
A = \begin{bmatrix}
a_{0,0} & a_{0,1} & & & & & & & & & & & & & & a_{0,15}\\
a_{1,0} & a_{1,1} & & & & & & & & & & & & & a_{1,14}\\
& & a_{2,2} & a_{2,3} & & & & & & & & & & a_{2,13} \\
& & a_{3,2} & a_{3,3} & & & & & & & & & a_{3,12}\\
& & & & a_{4,4} & a_{4,5} & & & & & & a_{4,11}\\
& & & & a_{5,4} & a_{5,5} & & & & & a_{5,10}\\
& & & & & & a_{6,6} & a_{6,7} & & a_{6,9}\\
& & & & & & a_{7,6} & a_{7,7} & a_{7,8}\\
& & & & & & & a_{8,7}& a_{8,8} & a_{8,9}\\
& & & & & & a_{9,6}& & a_{9,8} & a_{9.9} &\\
& & & & & a_{10,5} & & & & & a_{10,10} & a_{10,11} \\
& & & & a_{11,4} & & & & & & a_{11,10} & a_{11,11} & \\
& & & a_{12,3} & & & & & & & & & a_{12,12} & a_{12,13} \\
& & a_{13,2} & & & & & & & & & & a_{13,12} & a_{13,13} &\\
& a_{14,1}& & & & & & & & & & & & & a_{14,14} & a_{14,15}\\
a_{15,0}& & & & & & & & & & & & & & a_{15,14} & a_{15,15} \\
\end{bmatrix}
C = \begin{bmatrix}
c_{0}\\
c_{1}\\
c_{2}\\
c_{3}\\
c_{4}\\
c_{5}\\
c_{6}\\
c_{7}\\
c_{8}\\
c_{9}\\
c_{10}\\
c_{11}\\
c_{12}\\
c_{13}\\
c_{14}\\
c_{15}\\
\end{bmatrix}
\begin{bmatrix}
a_{0,0} & a_{0,1} & a_{0,7}\\
a_{1,0} & a_{1,1} & a_{1,6}\\
a_{2,2} & a_{2,3} & a_{2,5} \\
a_{3,2} & a_{3,3} & a_{3,4}\\
a_{4,3} & a_{4,4} & a_{4,5}\\
a_{5,2} & a_{5,5} & a_{5,5} \\
a_{6,1} & a_{6,6} & a_{6,7} \\
a_{7,0} & a_{7,6} & a_{7,7}\\
\end{bmatrix}
\begin{bmatrix}
c_{0}\\
c_{1}\\
c_{2}\\
c_{3}\\
c_{4}\\
c_{5}\\
c_{6}\\
c_{7}\\
\end{bmatrix}
P = \begin{bmatrix}
& p_{1} \\
p_{0} \\
& & & p_{3} &\\
& & p_{2} &\\
& & & & & p_{5} &\\
& & & & p_{4} &\\
& & & & & & & p_{7} &\\
& & & & & & p_{6} &\\
& & & & & & & & & p_{9} &\\
& & & & & & & & p_{8} &\\
& & & & & & & & & & & p_{11} &\\
& & & & & & & & & & p_{10} &\\
& & & & & & & & & & & & & p_{13} &\\
& & & & & & & & & & & & p_{12} &\\
& & & & & & & & & & & & & & & p_{15} \\
& & & & & & & & & & & & & & p_{14} &\\
\end{bmatrix}
P = \begin{bmatrix}
& & & p_{3} &\\
& & p_{2} &\\
& p_{1} & &\\
p_{0} & & & \\
& & & & & & & p_{7} &\\
& & & & & & p_{6} &\\
& & & & & p_{5} &\\
& & & & p_{4} &\\
& & & & & & & & & & & p_{11} &\\
& & & & & & & & & & p_{10} &\\
& & & & & & & & & p_{9} &\\
& & & & & & & & p_{8} &\\
& & & & & & & & & & & & & & & p_{15}\\
& & & & & & & & & & & & & & p_{14} &\\
& & & & & & & & & & & & & p_{13} &\\
& & & & & & & & & & & & p_{12} &\\
\end{bmatrix}
P = \begin{bmatrix}
& & & & p_{4} &\\
& & & & & p_{5} &\\
& & & & & & p_{6} &\\
& & & & & & & p_{7} &\\
p_{0} & & & \\
& p_{1} & &\\
& & p_{2} &\\
& & & p_{3} &\\
& & & & & & & & & & & & p_{12} &\\
& & & & & & & & & & & & & p_{13} &\\
& & & & & & & & & & & & & & p_{14} &\\
& & & & & & & & & & & & & & & p_{15} \\
& & & & & & & & p_{8} &\\
& & & & & & & & & p_{9} &\\
& & & & & & & & & & p_{10} &\\
& & & & & & & & & & & p_{11} &\\
\end{bmatrix}
P = \begin{bmatrix}
& & & & & p_{5} &\\
& & & & p_{4} &\\
& & & & & & & p_{7} &\\
& & & & & & p_{6} &\\
& p_{1} & &\\
p_{0} & & & \\
& & & p_{3} &\\
& & p_{2} &\\
& & & & & & & & & & & & & p_{13} &\\
& & & & & & & & & & & & p_{12} &\\
& & & & & & & & & & & & & & & p_{15} \\
& & & & & & & & & & & & & & p_{14} &\\
& & & & & & & & & p_{9} &\\
& & & & & & & & p_{8} &\\
& & & & & & & & & & & p_{11} &\\
& & & & & & & & & & p_{10} &\\
\end{bmatrix}
H = \begin{bmatrix}
& & & & & & & & & & & & & & & p_{15} \\
& & & & & & & & & & & & & & p_{14} &\\
& & & & & & & & & & & & & p_{13} &\\
& & & & & & & & & & & & p_{12} &\\
& & & & & & & & & & & p_{11} &\\
& & & & & & & & & & p_{10} &\\
& & & & & & & & & p_{9} &\\
& & & & & & & & p_{8} &\\
& & & & & & & p_{7} &\\
& & & & & & p_{6} &\\
& & & & & p_{5} &\\
& & & & p_{4} &\\
& & & p_{3} &\\
& & p_{2} &\\
& p_{1} & &\\
p_{0} & & & \\
\end{bmatrix}
\(a_1\)
\(a_2\)
\(a_3\)
\(\vdots\)
\(a_n\)
\(b_1\)
\(b_2\)
\(b_3\)
\(b_n\)
\(\vdots\)
\(a_1 - b_1\)
\(a_2 - b_2\)
\(a_3 - b_3\)
\(\vdots\)
\(a_n-b_n\)
$$\rho = \begin{bmatrix} a_{11} & \ldots & a_{1n} \\ \vdots & \ddots & \vdots\\ a_{1n} & \ldots & a_{nn} \end{bmatrix} = VDV^\dagger$$
deck
By ludmilaasb
deck
- 11
