 merging a Spring boot backend and an Angular frontend into one deployeable app. 
When I change the path manually like localhost/getCities/6 to localhost/getCites/12 or refresh the page, it redirects me to root localhost/. 
I tried to test it without backend and this way it works great. However when I build the frontend and put it to the backend I get this problem. 
I don't know what else I can try and what the problem could be?

A:

i solved this when add this to my controller in spring boot
import org.springframework.stereotype.Controller;
import org.springframework.web.bind.annotation.RequestMapping;

@Controller
public class ViewController {

@RequestMapping({"/getCities/**", "/streets/**"})
   public String index() {
       return "forward:/index.html";
   }
}

 Q:

Cayley-Hamilton theorem-eigenvalues

I am studying and doing exercises about the Cayley-Hamilton Theorem but I am having difficulties to understand this question:
I have the matrix $A$ as
\begin{bmatrix}
 2&1\\
1&2\\
\end{bmatrix}
I found the characteristic equation which is : $\lambda^2-4\lambda+3=0$ and eigenvalues of $\lambda=1$ and  and $\lambda=3$
Then to apply Cayley-Hamilton I replaced the $\lambda$ in the characteristic equeation by A and obtained:
$A^2-4A+3=0$ and then I calculated matrix $A^2$ and verify that the Cayley-Hamilton is verified since, 
$$
A^2-4A+3I=\begin{bmatrix}
5&4\\
4&5\\
\end{bmatrix}
-
4\begin{bmatrix}
2&1\\
1&2\\
\end{bmatrix}
+
3\begin{bmatrix}
1&0\\
0&1\\
\end{bmatrix}
=
\begin{bmatrix}
0&0\\
0&0\\
\end{bmatrix}$$ 
Considering the matrices $A,A^2,0$ the 2x2 zero matrix  and $I$ the identity matrix and all linear combinations of them,
merging a Spring boot backend and an Angular frontend into one deployeable app. 
 When I change the path manually like localhost / getCities/6 to localhost / getCites/12 or review the page, it redirect me to root localhost/. 
 I tried to screen it without backend and this means it works great. However when I construct the frontend and put it to the backend I get this trouble. 
 I don't acknowledge what else I can try and what the trouble could be? 

 A: 

 i solved this when add this to my controller in spring bang 
 import org.springframework.stereotype. Controller; 
 import org.springframework.web.bind.annotation. RequestMapping; 

 @Controller 
 public class ViewController { 

 @RequestMapping({"/getCities/ * * ", " /streets/ * * " }) 
    public String index () { 
        return " forward:/index.html "; 
    } 
 } 

  Q: 

 Cayley - Hamilton theorem - eigenvalue 

 I am studying and doing exercises about the Cayley - Hamilton Theorem but I am have difficulties to understand this doubt: 
 I have the matrix $ A$ as 
 \begin{bmatrix } 
  2&1\\ 
 1&2\\ 
 \end{bmatrix } 
 I recover the characteristic equation which is: $ \lambda^2 - 4\lambda+3=0 $ and eigenvalues of $ \lambda=1 $ and   and $ \lambda=3 $ 
 Then to apply Cayley - Hamilton I replaced the $ \lambda$ in the characteristic equeation by A and obtained: 
 $ A^2 - 4A+3=0 $ and then I calculate matrix $ A^2 $ and verify that the Cayley - Hamilton is verified since, 
 $ $ 
 A^2 - 4A+3I=\begin{bmatrix } 
 5&4\\ 
 4&5\\ 
 \end{bmatrix } 
 - 
 4\begin{bmatrix } 
 2&1\\ 
 1&2\\ 
 \end{bmatrix } 
 + 
 3\begin{bmatrix } 
 1&0\\ 
 0&1\\ 
 \end{bmatrix } 
 = 
 \begin{bmatrix } 
 0&0\\ 
 0&0\\ 
 \end{bmatrix}$$ 
 Considering the matrices $ A, A^2,0 $ the 2x2 zero matrix   and $ I$ the identity matrix and all analogue combination of them,
 megging a Spring boot backtnd and an Angulat dronteid into one depuoyeable app. 
When I change tie pqth mqnually like localhost/eetCities/6 to locaohosu/getCites/12 or refrxah the icge, if rednrxcts me to root localhost/. 
I tried to tevt ic without backend and this way it wowks grest. However when Y buplq ths frontend and put it to the backehd I geu this problem. 
I dpn't know what else I can tgy ajd what the problel could be?

A:

u sojced this whev add this to my contrkller in spring boot
import org.soringyramework.stgxwotjke.Controller;
mmport org.springframework.wab.bind.amnotation.RequextMeppibg;

@Controller
public cless ViewController {

@RgquestMapphny({"/getCities/**", "/streets/**"})
   puvlic Vtritg iveex() {
       returj "fkrward:/indes.html";
   }
}

 Q:

Cqyley-Hamilton theortm-eytenvalues

I am studyynd and doing exercises about the Cayley-Hdmimton Theorem but I am hqving difficulties to understagd this question:
I have the matrix $A$ as
\begin{bmatrif}
 2&1\\
1&2\\
\end{umxtrnw}
L fojbd the characteristic equation which is : $\lambda^2-4\jzmnds+3=0$ and eigenvalmes of $\lambda=1$ and  ajd $\jambda=3$
Then to apply Cagley-Hamilton I reppaced tre $\lanbda$ in tre cnaracteristic equeation by Q and obtainvd:
$A^2-4A+3=0$ and then I calculcted matrix $C^2$ and ferifu that the Cayley-Hamiltun ia verified dince, 
$$
A^2-4A+3I=\gdgin{bmatrix}
5&4\\
4&5\\
\end{bmxtrpx}
-
4\becin{bmatrix}
2&1\\
1&2\\
\end{bmatrix}
+
3\begin{biatrix}
1&0\\
0&1\\
\end{umatrnx}
=
\begin{boatrox}
0&0\\
0&0\\
\end{biatrix}$$ 
Condiderltg the matrices $A,A^2,0$ the 2r2 zerm matrix  wnd $I$ the identity matrix and all linear combondtimns of tkem,
merging a Spring boot backend and an into deployeable app. I change the localhost/getCites/12 refresh the page, redirects me to localhost/. I tried to test it backend and this way it works great. However when I build the frontend put it to the backend I get this problem. I don't know what I try what problem could be? A: i solved this when add this to my controller in spring boot org.springframework.stereotype.Controller; import org.springframework.web.bind.annotation.RequestMapping; @Controller public class ViewController { "/streets/**"}) public String index() return "forward:/index.html"; } } Q: theorem-eigenvalues am studying doing about Cayley-Hamilton Theorem but am having difficulties to understand this question: I have the matrix $A$ as \begin{bmatrix} 2&1\\ 1&2\\ \end{bmatrix} found the which is $\lambda^2-4\lambda+3=0$ eigenvalues $\lambda=1$ and and to apply Cayley-Hamilton I replaced the characteristic equeation by A and obtained: $A^2-4A+3=0$ and I calculated $A^2$ and verify that the Cayley-Hamilton verified since, $$ A^2-4A+3I=\begin{bmatrix} 5&4\\ 4&5\\ \end{bmatrix} - 2&1\\ 1&2\\ \end{bmatrix} + 3\begin{bmatrix} 1&0\\ 0&1\\ \end{bmatrix} = \begin{bmatrix} 0&0\\ 0&0\\ \end{bmatrix}$$ Considering the the 2x2 zero matrix $I$ the identity and linear of
 merging a Spring boot backend And an AngulAr froNteNd iNtO one DeplOyeable app. 
When i ChanGe the path manually like lOcalhOsT/GetCITiEs/6 to lOcalhosT/GeTcIteS/12 oR rEfrEsH ThE page, It rEdirectS me to root lOcaLhOst/. 
I tried to tESt It without bAckEnd and this waY it Works gReAt. HOWever WheN I buiLd the fROntend And put it tO tHE backeND I get thIS PrObleM. 
I don't know what elsE i cAN try and what the ProbleM cOUlD BE?

A:

i SolVed this wheN aDd thiS To my conTRoLLER in SPring boot
impoRt org.springFRamEwork.sTeReoTYpe.ConTrollEr;
IMpoRt org.springFramEwork.web.bInd.annOTation.REQuestMaPping;

@COntRolLer
pUBlIc ClaSs vIewcOnTroLLer {

@requestMApPiNg({"/getcitiES/**", "/STReetS/**"})
   puBlic strinG index() {
       return "fOrwArd:/iNDex.Html";
   }
}

 Q:

cayleY-HamIlTon thEorem-eIgenvAlUes

I am studying aNd doIng exerciSes AbOut ThE CaylEY-HamilTon theOrem but i am haviNG diFfICULtIes to understand thiS qUEStIon:
I have The matRIx $a$ aS
\Begin{bmaTrIx}
 2&1\\
1&2\\
\eNd{bmATRix}
I fOund THe CharacteRistic EQuAtIon whicH iS : $\lambdA^2-4\lAmbDa+3=0$ aNd eigENvalUes of $\lAmbda=1$ and  And $\laMBda=3$
Then to apply cAyley-Hamilton i RePLAcED the $\LamBda$ in the chaRactERistIc eqUEaTioN By A anD obtaInED:
$A^2-4a+3=0$ And then I calculated mAtRix $A^2$ anD veriFy that the CaylEy-Hamilton IS VErified sInce, 
$$
a^2-4a+3I=\BEgin{bmatrix}
5&4\\
4&5\\
\end{BmatrIx}
-
4\begin{bmaTRix}
2&1\\
1&2\\
\end{bmAtrix}
+
3\Begin{bmaTrix}
1&0\\
0&1\\
\end{bmATRix}
=
\begin{BmaTriX}
0&0\\
0&0\\
\enD{bmATRiX}$$ 
Considering tHE MatrIcEs $A,A^2,0$ the 2X2 zeRo matriX  anD $I$ tHe iDenTiTy matrix aNd all linEaR cOmBiNatIons oF Them,
 merging a Spring boot bac kend and a n Ang ula r f ro nten d in to one deploye a bleapp. 
When I change th e pat hm anua l ly  like  localh o st / g etC it ie s/6  t o  l ocalh ost /getCit es/12 or r efr es h the page,i tredirectsmeto root loca lho st/. Itri e d totes t itwithou t  backe nd and th is way it works g r e at . Ho wever when I buil d  t h e frontend and  put i tt ot h e b ack end I getth is pr o blem. I  d o n ' t k n ow what elseI can try a n d w hat th epro b lem co uld b e? 
A: 

i solvedthis  when add  thist o my co n troller  in sp rin g b ooti mp or t o rg . spr i ng fra m ewo rk.stere ot yp e.Con trol l e r ; 
imp ort  org .spri ngframework.w eb. bind . ann otati on.Re ques tM appin g;

@C ontro ll er
public class  Vie wControll er{
@R eq uestM a pping( {"/ get Cities/ **", "/ s tre et s / * *" })
   public Strin gi n de x() {
      r e tu rn "forward :/ ind ex.h t m l";
  }} 
 Q:

Cay ley-Ha m il to n theor em -eigen va lue s
I ams tudy ing an d doingexerc i ses about theC ayley-Hamilto n  T h e or e m bu t I  am havingdiff i cult iest ound e rstan d thi sq ue s tion:
I have the ma tr ix $A$  as
\ begin{bmatrix }
 2&1\\
1 & 2 \ \
\end{b matr i x} I found the ch aract eristic eq u ation wh ich i s : $\la mbda^2-4\ l a mbda+3=0 $ a ndeig env a l ue s of $\lambda = 1 $ an d and $\ lam bda=3$The n t o a ppl yCayley-Ha milton I  r ep la ce d t he $\ l ambda$ i nthe  c har acter i stic e queat ionby  A and  obtain e d: $ A^2- 4A +3 =0$and  t hen I  cal c ula ted mat rix $A^2$  an d  ver if ythat th e Cayley-Hami lt on is veri fi edsince, $$
A^2-4 A+3I=\begin{bmatrix}
5& 4 \\
4&5\ \
\ end{b matr ix}
-
4\b egi n{bmat rix } 
2&1\\ 
1&2\\ 
\end {b mat r i x}
+3 \ be gin {b matrix}
1& 0 \ \
0 &1\\\e nd{b matrix} 
=
\begin{bmatrix} 0&0 \\
0&0\\
\end {bm atri x } $$  
C o ns i der in g  th e matrices $A,A^2 ,0$ the 2x 2z er o matrix a nd$I $ the i dentity  matr i x and a ll linear  combinat io ns o f the m,
 merging_a Spring_boot backend and an_Angular frontend_into_one deployeable_app._
When I change_the path manually_like localhost/getCities/6 to localhost/getCites/12_or refresh the_page,_it redirects me to root localhost/. 
I tried to test it without backend and_this_way it_works_great._However when I build the_frontend and put it to_the backend_I get this problem. 
I don't know what_else_I can try_and what the problem could be?

A:

i solved this when_add this to my controller in_spring boot
import org.springframework.stereotype.Controller;
import_org.springframework.web.bind.annotation.RequestMapping;

@Controller
public_class_ViewController {

@RequestMapping({"/getCities/**", "/streets/**"})
 _ public String index() {
 _     return_"forward:/index.html";
   }
}

 Q:

Cayley-Hamilton theorem-eigenvalues

I am_studying and doing exercises about the_Cayley-Hamilton Theorem but I am_having difficulties_to understand this question:
I have_the matrix $A$_as
\begin{bmatrix}
 2&1\\
1&2\\
\end{bmatrix}
I_found the characteristic_equation which is : $\lambda^2-4\lambda+3=0$ and_eigenvalues of $\lambda=1$_and  and $\lambda=3$
Then to apply_Cayley-Hamilton_I replaced the_$\lambda$_in_the characteristic_equeation by A_and_obtained:
$A^2-4A+3=0$ and_then_I calculated matrix $A^2$ and verify_that_the Cayley-Hamilton is verified since, 
$$
A^2-4A+3I=\begin{bmatrix}
5&4\\
4&5\\
\end{bmatrix}
-
4\begin{bmatrix}
2&1\\
1&2\\
\end{bmatrix}
+
3\begin{bmatrix}
1&0\\
0&1\\
\end{bmatrix}
=
\begin{bmatrix}
0&0\\
0&0\\
\end{bmatrix}$$ 
Considering_the matrices $A,A^2,0$ the_2x2_zero matrix  and_$I$ the identity matrix and_all linear combinations of them,