...As this scene here. 
The sand in the room, or rather, Cooper was able to draw the lines, himself through an anomaly in gravity, or gravity waves, and putting his hand in between,'stopping' gravity from working in those positions, and the sand falling down. As seen here :)

 Q:

How can I get the following equation w.r.t. positive semidefinite symmetric matrix?

There are matrices; $x_k$, $u_k$, $A_k$, $B_k$, and $Q_k$ whose dimension are $[n\times1]$, $[m\times1]$, $[n\times n]$, $[n\times m]$, and $[n\times n]$, respectively, such that $$x_{k+1}=A_kx_k+B_ku_k+w_k.$$
Another condition is that the matrices $Q_k$ are positive semidefinite symmetric.

My textbook jumped from the equation (1) to the equation (2), regarding very natural and of course.
$$
\mathbf{E}\left(A_{N-1}x_{N-1}+B_{N-1}u_{N-1}+w_{N-1}\right)'Q_N\left(A_{N-1}x_{N-1}+B_{N-1}u_{N-1}+w_{N-1}\right) \tag1
$$
$$
u'_{N-1}B'_{N-1}Q_NB_{N-1}u_{N-1}+2x'_{N-1}A'_{N-1}Q_NB_{N-1}u_{N-1}+x'_{N-1}A'_{N-1}Q_NA_{N-1}x_{N-1}+\mathbf{E}\left(w'_{N-1}Q_Nw_{N-1}\right) \tag 2
$$

But I don't say before that the matrices $w_k$ whose each element has zero-mean distribution. I can follow almost steps except that how can it become
$$x'_{N-1}A'_{N-1}Q_NB_{N-1}u_{N-1}+u'_{N-1}B'_{N-1}Q_NA_{N-1}x_{N-1} =
... As this scene here. 
 The sand in the room, or rather, Cooper was able to draw the occupation, himself through an anomaly in graveness, or gravity waves, and frame his handwriting in between,'stopping' gravity from working in those position, and the backbone falling down. As seen here :) 

  Q: 

 How can I get the following equation w.r.t. positivist semidefinite symmetric matrix? 

 There are matrices; $ x_k$, $ u_k$, $ A_k$, $ B_k$, and $ Q_k$ whose proportion are $ [ n\times1]$, $ [ m\times1]$, $ [ n\times n]$, $ [ n\times m]$, and $ [ n\times n]$, respectively, such that $ $ x_{k+1}=A_kx_k+B_ku_k+w_k.$$ 
 Another circumstance is that the matrices $ Q_k$ are positive semidefinite symmetric. 

 My textbook jump from the equation (1) to the equation (2), see very natural and of course. 
 $ $ 
 \mathbf{E}\left(A_{N-1}x_{N-1}+B_{N-1}u_{N-1}+w_{N-1}\right)'Q_N\left(A_{N-1}x_{N-1}+B_{N-1}u_{N-1}+w_{N-1}\right) \tag1 
 $ $ 
 $ $ 
 u'_{N-1}B'_{N-1}Q_NB_{N-1}u_{N-1}+2x'_{N-1}A'_{N-1}Q_NB_{N-1}u_{N-1}+x'_{N-1}A'_{N-1}Q_NA_{N-1}x_{N-1}+\mathbf{E}\left(w'_{N-1}Q_Nw_{N-1}\right) \tag 2 
 $ $ 

 But I don't say before that the matrix $ w_k$ whose each element has zero - mean distribution. I can follow about steps except that how can it become 
 $ $ x'_{N-1}A'_{N-1}Q_NB_{N-1}u_{N-1}+u'_{N-1}B'_{N-1}Q_NA_{N-1}x_{N-1 } =
...As hhis scene here. 
The sand in the room, or rather, Cooped was abue to draw the lines, himself tyrougy an anomaly in gravith, or gravpty waves, and putting his hand ik betscen,'stm'ping' gravity ftom working hn those posithovs, and the sand falling down. As seen rere :)

 Q:

Noa can I get thg folkjwinf equation w.r.t. positive semidefinife symmttric matrix?

There sre matrices; $x_k$, $u_k$, $A_k$, $B_k$, ajd $Q_n$ whose dimension wre $[n\times1]$, $[n\timqw1]$, $[n\times n]$, $[n\gimes m]$, and $[n\times n]$, rgspectively, such that $$x_{k+1}=A_kx_k+B_ku_k+d_k.$$
Anocher condituob id that the metricef $Q_k$ are poslnive sekidefinote symmetric.

Mn texvbooj jumped from the equetion (1) to the equatijn (2), regargiug very natural and od xoursg.
$$
\mathtf{E}\lddt(A_{V-1}x_{N-1}+G_{N-1}n_{N-1}+w_{H-1}\right)'E_N\lxft(A_{N-1}x_{N-1}+B_{N-1}u_{N-1}+s_{N-1}\right) \tag1
$$
$$
y'_{N-1}B'_{N-1}Q_NB_{N-1}u_{N-1}+2x'_{N-1}A'_{N-1}Q_NB_{N-1}u_{M-1}+x'_{G-1}Q'_{N-1}Q_NA_{N-1}x_{N-1}+\mathbr{E}\left(r'_{N-1}Z_Nw_{N-1}\right) \tag 2
$$

But I don't say before thau the matrices $w_k$ whose each element has zero-mean distribueion. I can follow almost steps except that how cat it uezomt
$$x'_{K-1}W'_{V-1}W_NH_{N-1}u_{N-1}+u'_{N-1}B'_{N-1}Q_NA_{N-1}x_{N-1} =
...As this scene here. The sand in or Cooper was to draw the in or gravity waves, putting his hand between,'stopping' gravity from working in those and the sand falling down. As seen here :) Q: How can I the following equation w.r.t. positive semidefinite symmetric matrix? There are matrices; $x_k$, $u_k$, $B_k$, $Q_k$ dimension $[n\times1]$, $[m\times1]$, $[n\times n]$, $[n\times m]$, and $[n\times n]$, respectively, such that $$x_{k+1}=A_kx_k+B_ku_k+w_k.$$ Another condition is the matrices $Q_k$ are positive semidefinite symmetric. My jumped from the equation to the equation (2), regarding natural of course. \mathbf{E}\left(A_{N-1}x_{N-1}+B_{N-1}u_{N-1}+w_{N-1}\right)'Q_N\left(A_{N-1}x_{N-1}+B_{N-1}u_{N-1}+w_{N-1}\right) $$ u'_{N-1}B'_{N-1}Q_NB_{N-1}u_{N-1}+2x'_{N-1}A'_{N-1}Q_NB_{N-1}u_{N-1}+x'_{N-1}A'_{N-1}Q_NA_{N-1}x_{N-1}+\mathbf{E}\left(w'_{N-1}Q_Nw_{N-1}\right) \tag 2 But I don't say before that the matrices $w_k$ whose each element has zero-mean distribution. I can almost steps how can become =
...As this scene here. 
The sand in tHe room, or raTher, COopEr wAs Able To drAw the lines, himsELf thRough an anomaly in gravitY, or grAvITy waVEs, And puTting hiS HaND In bEtWeEn,'sToPPiNg' graVitY from woRking in thoSe pOsItions, and the SAnD falling doWn. AS seen here :)

 Q:

HoW caN I get tHe FolLOwing EquAtion W.r.t. posITive seMidefinitE sYMmetriC Matrix?

THERe Are mAtrices; $x_k$, $u_k$, $A_k$, $B_k$, anD $q_k$ WHose dimension aRe $[n\timEs1]$, $[M\TiMES1]$, $[n\tImeS n]$, $[n\times m]$, aNd $[N\timeS N]$, respecTIvELY, SucH That $$x_{k+1}=A_kx_k+B_ku_K+w_k.$$
Another cONdiTion is ThAt tHE matriCes $Q_k$ ArE PosItive semideFiniTe symmetrIc.

My teXTbook juMPed from The equAtiOn (1) tO the EQuAtIon (2), ReGArdINg VerY NatUral and oF cOuRse.
$$
\maThbf{e}\LEFT(A_{N-1}x_{n-1}+B_{N-1}U_{N-1}+w_{N-1}\Right)'q_N\left(A_{N-1}x_{N-1}+B_{N-1}u_{n-1}+w_{N-1}\RighT) \Tag1
$$
$$
U'_{N-1}B'_{N-1}Q_nB_{N-1}u_{N-1}+2X'_{N-1}A'_{N-1}q_Nb_{N-1}u_{N-1}+x'_{n-1}A'_{N-1}Q_NA_{n-1}x_{N-1}+\maThBf{E}\left(w'_{N-1}Q_Nw_{N-1}\riGht) \tAg 2
$$

But I don'T saY bEfoRe That tHE matriCes $W_k$ wHose eacH elemenT Has ZeRO-MEaN distribution. I can fOlLOW aLmost stePs excePT tHaT How can it BeComE
$$x'_{N-1}A'_{n-1}q_nB_{N-1}u_{N-1}+U'_{N-1}B'_{N-1}q_nA_{n-1}x_{N-1} =
...As this scene here. 
Th e sand inthe r oom , o rrath er,Cooper was abl e  todraw the lines, himsel f thr ou g h an an omaly  in gra v it y ,  or  g ra vit yw av es, a ndputting  his handinbe tween,'stopp i ng ' gravityfro m working in  th ose po si tio n s, an d t he sa nd fal l ing do wn. As se en here : ) 

 Q:
H o wcanI get the followi n ge quation w.r.t.  posit iv e  s e m ide fin ite symmet ri c mat r ix?

Th e re a r e m a trices; $x_k$ , $u_k$, $A _ k$,  $B_k$ ,and $Q_k$whose  d i men sion are $[ n\ti mes1]$, $ [m\tim e s1]$, $ [ n\times  n]$,$[n \ti mesm ]$ ,and  $ [ n\t i me s n ] $,respecti ve ly , suc h th a t $ $x_{ k+1 }=A_ kx_k+ B_ku_k+w_k.$$ 
An othe r  co nditi on is  tha tthe m atrice s $Q_ k$  are positive s emid efinite s ymm et ric .
My t e xtbook  ju mpe d fromthe equ a tio n( 1 )  t o the equation (2) ,r e ga rding ve ry nat u ra la nd of co ur se. 
$$\ m athbf {E}\ l ef t(A_{N-1 }x_{N- 1 }+ B_ {N-1}u_ {N -1}+w_ {N -1} \ri ght)' Q _N\l eft(A_ {N-1}x_{ N-1}+ B _{N-1}u_{N-1}+ w _{N-1}\right) \t a g 1$ $
$$ 
u' _{N-1}B'_{N -1}Q _ NB_{ N-1} u _{ N-1 } +2x'_ {N-1} A' _ {N - 1}Q_NB_{N-1}u_{N-1} +x '_{N-1 }A'_{ N-1}Q_NA_{N-1 }x_{N-1}+\ m a t hbf{E}\l eft( w '_ { N-1}Q_Nw_{N-1} \righ t) \tag 2$ $

But I  don' t say be fore that t he matri ces  $w _k$  wh o s eeach elementh a s ze ro -mean d ist ributio n.I c anfol lo w almoststeps ex ce pt  t ha t h ow ca n  it beco me 
$$ x' _{N -1}A' _ {N-1}Q _NB_{ N-1} u_ {N - 1}+ u'_{N-1 } B' _ { N-1} Q_ NA _{N- 1}x _{ N-1}=
...As this_scene here._
The sand in the_room, or_rather,_Cooper was_able_to draw the_lines, himself through_an anomaly in gravity,_or gravity waves,_and_putting his hand in between,'stopping' gravity from working in those positions, and the sand_falling_down. As_seen_here_:)

 Q:

How can I get_the following equation w.r.t. positive_semidefinite symmetric_matrix?

There are matrices; $x_k$, $u_k$, $A_k$, $B_k$, and_$Q_k$_whose dimension are_$[n\times1]$, $[m\times1]$, $[n\times n]$, $[n\times m]$, and $[n\times n]$,_respectively, such that $$x_{k+1}=A_kx_k+B_ku_k+w_k.$$
Another condition is_that the matrices_$Q_k$_are_positive semidefinite symmetric.

My textbook_jumped from the equation (1) to_the equation (2), regarding very natural_and of course.
$$
\mathbf{E}\left(A_{N-1}x_{N-1}+B_{N-1}u_{N-1}+w_{N-1}\right)'Q_N\left(A_{N-1}x_{N-1}+B_{N-1}u_{N-1}+w_{N-1}\right) \tag1
$$
$$
u'_{N-1}B'_{N-1}Q_NB_{N-1}u_{N-1}+2x'_{N-1}A'_{N-1}Q_NB_{N-1}u_{N-1}+x'_{N-1}A'_{N-1}Q_NA_{N-1}x_{N-1}+\mathbf{E}\left(w'_{N-1}Q_Nw_{N-1}\right) \tag 2
$$

But I_don't say before that the matrices_$w_k$ whose each element has_zero-mean distribution._I can follow almost steps_except that how_can it_become
$$x'_{N-1}A'_{N-1}Q_NB_{N-1}u_{N-1}+u'_{N-1}B'_{N-1}Q_NA_{N-1}x_{N-1} =