how to solve matrix equation?

Question

Nara Lee 2021-4-18

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/805746-how-to-solve-matrix-equation

回答： Nara Lee 2021-4-24

I want to solve a equation which has vector known elements and obvisouly the answer should be vector too.

x1=sym('x1',[121 1]);
x2=sym('x2',[121 1]);
s=solve(x1+x2==n1,x1.*x2==n2,[x1,x2]);

but I think I didn't write the right code coz it's been a long time that is busy and there is no answer yet. I really need your help.

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Answer 1

Walter Roberson 2021-4-22

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https://ww2.mathworks.cn/matlabcentral/answers/805746-how-to-solve-matrix-equation#answer_681785

在 MATLAB Online 中打开

x1+x2=n1
x1*x2=n2

so

x2 = n1-x1
x1*(n1-x1) = n2
x1*n1-x1^2 = n2
x1^2 - x1*n1 + n2 = 0

and solve the quadratic to get x1 and then x2. There will be two solutions

Do this just for scalars to get the forms of the solutions. Then substitute in the vectors.

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Nara Lee 2021-4-24

the thing is I have a matrix that is not square matrix[242 2]

and i want it to be inverse then i thought if A*A(inv)=1

So I create a matrix [242 2] that gives me what i want when A*A(inv) is done. then u*x=my creation would give me x that is my inverse matrix

and i ran your code and it didn't work.

Walter Roberson 2021-4-24

在 MATLAB Online 中打开

format long g
A = rand(42,2);
Ainv = pinv(A);
Ainv * A
ans = 2×2
                         1     -5.20417042793042e-17
     -1.38777878078145e-16                         1
ans = 42×42
         0.122279499034516         0.100591415380188        0.0828882943136175       0.00950733225267564        0.0643791627164946       -0.0495366330834786        0.0323927791469979        0.0810689532034453       0.00723859743041875        0.0614055106488573        0.0281472612408997        0.0103958103260886       0.00419121852178334      0.000443856252444105        0.0633644133018594        0.0572660502092225       -0.0254592276700414       -0.0671865361348825        0.0356470256968464       -0.0325611918191314        -0.062762560254855        0.0600155324726122      -0.00745774679471391        0.0933225155629304       -0.0677605311147749        0.0310572199058558      0.000683735860166118          0.12114679354168        0.0273682604229063       -0.0404960035255129
         0.100591415380188        0.0829323704379949        0.0671784619264675       0.00686127541624179         0.051411844803746       -0.0437212376649601        0.0235735210496245        0.0659541224550693       0.00525255992838871        0.0477855609641493        0.0223442937564653       0.00568785007493196      0.000266661405490322      -0.00275641820738351        0.0510668476915052        0.0461221570017992       -0.0233792013966787        -0.058375424067824         0.028221149304995       -0.0288838344190183       -0.0548217641902133        0.0482861285754476      -0.00905003890961012        0.0758062479048013       -0.0591438163935129        0.0255235904715697      -0.00177157151383935        0.0999838350490465        0.0205094679794906       -0.0366189810000271
        0.0828882943136175        0.0671784619264675        0.0617631236862641        0.0117525348413641         0.052204844907584       -0.0171503022235395        0.0389573474528528        0.0590238933310336       0.00878991265227885        0.0567151411633483        0.0235629031940631        0.0228861970008722        0.0204338581827212        0.0175638907691266        0.0488084185981191        0.0442762011716884      -0.00378854597924713       -0.0283692181141537        0.0302654782479146       -0.0104702089864427       -0.0248966716877106        0.0466810959627405        0.0110656273479028        0.0685914607665231        -0.027120218119098        0.0211916254144342        0.0133713330985715        0.0803274379804908        0.0296379518653182      -0.00917003311669867
       0.00950733225267566        0.0068612754162418        0.0117525348413641       0.00579142182426778        0.0131577952624963        0.0117856837819247        0.0186992929943493        0.0101776494529567       0.00425891652240739        0.0191382461181393       0.00645554570367515        0.0158846015441607        0.0170712243185868        0.0164659664176226        0.0105008008785478       0.00964745303468412        0.0108409370383402         0.011122725974723       0.00857947126307491       0.00851118207049477        0.0119175881943944        0.0103762938028744        0.0147645364323098        0.0123309897232221         0.012637278253383       0.00254721964630818        0.0123392438508897       0.00771259317015302        0.0126800068632322        0.0142513837172234
        0.0643791627164946         0.051411844803746         0.052204844907584        0.0131577952624963        0.0470495989295207     -0.000848446856654554        0.0431637625556737         0.048933993283779       0.00977510640121653        0.0555071235024547          0.02170465453138        0.0298004625932581        0.0292269507348875        0.0267474900242421        0.0423553237778054        0.0385327158721362       0.00728294633092717      -0.00899639136739272        0.0281394754193564      0.000675530135516445      -0.00593964060131988        0.0408114070136169        0.0208332575559666        0.0573227081321525      -0.00678270029309243        0.0165651680688099        0.0201848087634951        0.0610289187169428        0.0314360420362163       0.00675579920859723
       -0.0495366330834786       -0.0437212376649601       -0.0171503022235395        0.0117856837819247     -0.000848446856654542        0.0684667042561843        0.0369585765492405       -0.0208499000875407       0.00850745657253676        0.0195819943012646       0.00180434722178253         0.042451493410837        0.0501308897338612        0.0506774347370917      -0.00841686763851576      -0.00712001280886565        0.0499944363637104        0.0778123331454642       0.00353511081681727         0.047369724514395        0.0774157068988091      -0.00663966601277362        0.0505138338307351       -0.0220978958293409        0.0828707081324624       -0.0121714990607543        0.0377498500728268       -0.0543601035818623        0.0215728155312605        0.0702602734308179
         0.032392779146998        0.0235735210496245        0.0389573474528528        0.0186992929943493        0.0431637625556737        0.0369585765492404        0.0604030683470199        0.0338845473007653         0.013755080171894        0.0622700690426726        0.0211225684139769        0.0510388148027409         0.054740584338676        0.0527425609781959        0.0346380841191454        0.0318081338588962         0.034315556853552        0.0345547724874134        0.0280440701852602        0.0267411689613347        0.0371707960738655        0.0341860941067182        0.0471677972758245        0.0409758186369918        0.0393963011045024       0.00865163794016675        0.0395297308317907        0.0266267684629125        0.0410452507251998        0.0449991707298244
        0.0810689532034453        0.0659541224550693        0.0590238933310336        0.0101776494529567         0.048933993283779       -0.0208499000875407        0.0338845473007653        0.0567184290513842       0.00763354197835819        0.0517261445507159        0.0219334466663459        0.0184540258379041        0.0156204589198864        0.0128953066778725        0.0462841300237181        0.0419502336889737      -0.00704719427071437        -0.032007466161975        0.0280872723183638       -0.0131188527015599       -0.0287286711319365        0.0441680841014552       0.00682303533499611        0.0657630391629541       -0.0311923012482871        0.0206919472594538       0.00987531724699025        0.0790091712989869        0.0262368791468966       -0.0135042844209968
       0.00723859743041877       0.00525255992838872       0.00878991265227885       0.00425891652240739       0.00977510640121653       0.00850745657253676         0.013755080171894       0.00763354197835819       0.00313250949992457        0.0141434060498184       0.00478794886709362        0.0116449573116017        0.0124986981604577        0.0120472235058898       0.00782894836697883        0.0071905305986783       0.00787206267385261       0.00798157028767676       0.00635914347893124       0.00615120842490258        0.0085733230374413       0.00773010501205235        0.0107841881246033       0.00923726604119257       0.00908825921105944       0.00193542975243093       0.00902874543056264        0.0059229761790014       0.00933984492253078        0.0103322557487092
        0.0614055106488573        0.0477855609641493        0.0567151411633483        0.0191382461181393        0.0555071235024547        0.0195819943012646        0.0622700690426726        0.0517261445507159        0.0141434060498184        0.0716741328870241        0.0262664810407564         0.048083841820535        0.0497132786978242        0.0469390143282528        0.0476677801980033        0.0435272585332005        0.0236646513502061        0.0127353914422157        0.0344133334554462        0.0150444371570581        0.0162389282125934        0.0463723554557685        0.0398803900221919        0.0612930167970301        0.0168800391577657        0.0159728050077307        0.0352738026206232        0.0559844775340679        0.0437441958302761        0.0291337114122371

It isn't clear what you mean when you say that you want A * Ainv = 1 for a non-square matrix. Do you mean a matrix with all ones? Do you mean a non-square matrix in which the main diagonal is 1 and the rest is 0? What size do you expect A*Ainv to be?

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