Find lower triangular matrix

I have this the equations LQLQx1x_1=b1=b_1 and LQLQx2x_2=b2=b_2. I need to find LL – the lower triangular matrix with comlex, non-negative and negative elements from first equation, and then find x2x_2 from second equation.
I know this elements:
QQ – Real orthogonal matrix (colums) [m×n][m\times{n}], m>nm>n;
x1x_1 – colum vector [n×1][n\times{1}];
b1,b2b_1,b_2 – complex colum vector [m×1][m\times{1}].
For example with delay 33 matrix LL must be [m×m][m\times{m}] with elements:

L=(l100⋯0l2l10⋯0l3l2l1⋯0⋮⋮⋮⋱⋮00l3l2l1) L =
\begin{pmatrix}
l_{1} & 0 & 0 &\cdots & 0 \\
l_{2} & l_{1} & 0 &\cdots & 0 \\
l_{3} & l_{2} & l_{1} &\cdots & 0 \\
\vdots & \vdots & \vdots& \ddots & \vdots\\
0 & 0 & l_{3} & l_{2} & l_{1}\\
\end{pmatrix}

because, b1(3)=Qx1+(Q)1×1+(Q)2x1b_1(3)=Qx_1+(Q)_1x_1+(Q)_2x_1 where (Q)h(Q)_h matrix [m×n][m\times{n}] with delay hh:

(Q)h=(000⋯0000⋯0⋮⋮⋮⋱⋮q1,1q1,2q1,3⋯q1,nq2,1q2,2q2,3⋯q2,n⋮⋮⋮⋱⋮qm−h,1qm−h,2qm−h,3⋯q1) (Q)_h =
\begin{pmatrix}
0 & 0 & 0 &\cdots & 0 \\
0 & 0 & 0 &\cdots & 0 \\
\vdots & \vdots & \vdots& \ddots & \vdots\\
q_{1,1} & q_{1,2} & q_{1,3} &\cdots & q_{1,n} \\
q_{2,1} & q_{2,2} & q_{2,3} &\cdots & q_{2,n} \\
\vdots & \vdots & \vdots& \ddots & \vdots\\
q_{m-h,1} & q_{m-h,2} & q_{m-h,3} &\cdots & q_{1} \\
\end{pmatrix}

It’s possible to find LL and x2x_2? Thank you!

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