Real valued vector representation of Hermitian matrixmatrix representation of operatorExtracting vector containing the elements of the main diagonal of a matrixThe dual representation matrix is the conjugate transpose of the rep matrix acting from right?Find an invertible real-valued matrix PPermutation between two vectorizations of a matrixConstruction of Hermitian Matrix originally over complex vector space with respect to real vector space.Find a real matrix $B$ such that $B^3 = A$Graphic representation of the complex eigenvector of a rotating matrixMatrix representation of complex number is just a trick?Help understanding the complex matrix representation of quaternions

How to draw a waving flag in TikZ

Paid for article while in US on F-1 visa?

Revoked SSL certificate

Was any UN Security Council vote triple-vetoed?

Could an aircraft fly or hover using only jets of compressed air?

What defenses are there against being summoned by the Gate spell?

Approximately how much travel time was saved by the opening of the Suez Canal in 1869?

Why "Having chlorophyll without photosynthesis is actually very dangerous" and "like living with a bomb"?

Perform and show arithmetic with LuaLaTeX

Client team has low performances and low technical skills: we always fix their work and now they stop collaborate with us. How to solve?

Why is 150k or 200k jobs considered good when there's 300k+ births a month?

What's the output of a record needle playing an out-of-speed record

What are these boxed doors outside store fronts in New York?

Do infinite dimensional systems make sense?

How to determine what difficulty is right for the game?

Is it tax fraud for an individual to declare non-taxable revenue as taxable income? (US tax laws)

Definite integral giving negative value as a result?

Modeling an IP Address

tikz convert color string to hex value

What would happen to a modern skyscraper if it rains micro blackholes?

"You are your self first supporter", a more proper way to say it

If human space travel is limited by the G force vulnerability, is there a way to counter G forces?

Can I make popcorn with any corn?

Fully-Firstable Anagram Sets



Real valued vector representation of Hermitian matrix


matrix representation of operatorExtracting vector containing the elements of the main diagonal of a matrixThe dual representation matrix is the conjugate transpose of the rep matrix acting from right?Find an invertible real-valued matrix PPermutation between two vectorizations of a matrixConstruction of Hermitian Matrix originally over complex vector space with respect to real vector space.Find a real matrix $B$ such that $B^3 = A$Graphic representation of the complex eigenvector of a rotating matrixMatrix representation of complex number is just a trick?Help understanding the complex matrix representation of quaternions













0












$begingroup$


Since my application is in physics, I created a specialized version of this question on physics.SE.



One can write a symmetric matrix $M in mathbbR, mathbbC^n times n$ in a half-vectorized representation, e.g.,
$$ M = beginbmatrix a & b\ b & c endbmatrix rightarrow vec m = beginbmatrix a\ b\ c endbmatrix, $$
where the resulting vector $vec m in mathbbR, mathbbC^n(n-1)/2$ is either real or complex valued. Similarly, one can exploit the redundant information in a Hermitian matrix. If the technique above is applied, the resulting vector is a mixture of real values (main diagonal terms) and complex values (off-diagonal terms). For the implementation in strongly typed programming languages, a completely real valued representation would be helpful. Now there are several degrees of freedom how to arrange the main diagonal terms, the real part terms, and the imaginary part terms in an array.



Is there a standard way to split the real and imaginary part of the off-diagonal terms and write the matrix $M$ as real valued vector $vec m in mathbbR^n^2$?



My approach would be to iterate over the matrix elements $M_ij$ and assign to the vector elements
$$
m_i + jN =
begincases M_ij, & i = j,\
ReM_ij, & i < j,\
ImM_ij, & i > j.
endcases
$$

Does this arrangement have a certain name?










share|cite|improve this question











$endgroup$
















    0












    $begingroup$


    Since my application is in physics, I created a specialized version of this question on physics.SE.



    One can write a symmetric matrix $M in mathbbR, mathbbC^n times n$ in a half-vectorized representation, e.g.,
    $$ M = beginbmatrix a & b\ b & c endbmatrix rightarrow vec m = beginbmatrix a\ b\ c endbmatrix, $$
    where the resulting vector $vec m in mathbbR, mathbbC^n(n-1)/2$ is either real or complex valued. Similarly, one can exploit the redundant information in a Hermitian matrix. If the technique above is applied, the resulting vector is a mixture of real values (main diagonal terms) and complex values (off-diagonal terms). For the implementation in strongly typed programming languages, a completely real valued representation would be helpful. Now there are several degrees of freedom how to arrange the main diagonal terms, the real part terms, and the imaginary part terms in an array.



    Is there a standard way to split the real and imaginary part of the off-diagonal terms and write the matrix $M$ as real valued vector $vec m in mathbbR^n^2$?



    My approach would be to iterate over the matrix elements $M_ij$ and assign to the vector elements
    $$
    m_i + jN =
    begincases M_ij, & i = j,\
    ReM_ij, & i < j,\
    ImM_ij, & i > j.
    endcases
    $$

    Does this arrangement have a certain name?










    share|cite|improve this question











    $endgroup$














      0












      0








      0





      $begingroup$


      Since my application is in physics, I created a specialized version of this question on physics.SE.



      One can write a symmetric matrix $M in mathbbR, mathbbC^n times n$ in a half-vectorized representation, e.g.,
      $$ M = beginbmatrix a & b\ b & c endbmatrix rightarrow vec m = beginbmatrix a\ b\ c endbmatrix, $$
      where the resulting vector $vec m in mathbbR, mathbbC^n(n-1)/2$ is either real or complex valued. Similarly, one can exploit the redundant information in a Hermitian matrix. If the technique above is applied, the resulting vector is a mixture of real values (main diagonal terms) and complex values (off-diagonal terms). For the implementation in strongly typed programming languages, a completely real valued representation would be helpful. Now there are several degrees of freedom how to arrange the main diagonal terms, the real part terms, and the imaginary part terms in an array.



      Is there a standard way to split the real and imaginary part of the off-diagonal terms and write the matrix $M$ as real valued vector $vec m in mathbbR^n^2$?



      My approach would be to iterate over the matrix elements $M_ij$ and assign to the vector elements
      $$
      m_i + jN =
      begincases M_ij, & i = j,\
      ReM_ij, & i < j,\
      ImM_ij, & i > j.
      endcases
      $$

      Does this arrangement have a certain name?










      share|cite|improve this question











      $endgroup$




      Since my application is in physics, I created a specialized version of this question on physics.SE.



      One can write a symmetric matrix $M in mathbbR, mathbbC^n times n$ in a half-vectorized representation, e.g.,
      $$ M = beginbmatrix a & b\ b & c endbmatrix rightarrow vec m = beginbmatrix a\ b\ c endbmatrix, $$
      where the resulting vector $vec m in mathbbR, mathbbC^n(n-1)/2$ is either real or complex valued. Similarly, one can exploit the redundant information in a Hermitian matrix. If the technique above is applied, the resulting vector is a mixture of real values (main diagonal terms) and complex values (off-diagonal terms). For the implementation in strongly typed programming languages, a completely real valued representation would be helpful. Now there are several degrees of freedom how to arrange the main diagonal terms, the real part terms, and the imaginary part terms in an array.



      Is there a standard way to split the real and imaginary part of the off-diagonal terms and write the matrix $M$ as real valued vector $vec m in mathbbR^n^2$?



      My approach would be to iterate over the matrix elements $M_ij$ and assign to the vector elements
      $$
      m_i + jN =
      begincases M_ij, & i = j,\
      ReM_ij, & i < j,\
      ImM_ij, & i > j.
      endcases
      $$

      Does this arrangement have a certain name?







      linear-algebra matrices vectors






      share|cite|improve this question















      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited Mar 22 at 16:10







      carlosvalderrama

















      asked Mar 21 at 19:41









      carlosvalderramacarlosvalderrama

      1388




      1388




















          0






          active

          oldest

          votes












          Your Answer





          StackExchange.ifUsing("editor", function ()
          return StackExchange.using("mathjaxEditing", function ()
          StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
          StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
          );
          );
          , "mathjax-editing");

          StackExchange.ready(function()
          var channelOptions =
          tags: "".split(" "),
          id: "69"
          ;
          initTagRenderer("".split(" "), "".split(" "), channelOptions);

          StackExchange.using("externalEditor", function()
          // Have to fire editor after snippets, if snippets enabled
          if (StackExchange.settings.snippets.snippetsEnabled)
          StackExchange.using("snippets", function()
          createEditor();
          );

          else
          createEditor();

          );

          function createEditor()
          StackExchange.prepareEditor(
          heartbeatType: 'answer',
          autoActivateHeartbeat: false,
          convertImagesToLinks: true,
          noModals: true,
          showLowRepImageUploadWarning: true,
          reputationToPostImages: 10,
          bindNavPrevention: true,
          postfix: "",
          imageUploader:
          brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
          contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
          allowUrls: true
          ,
          noCode: true, onDemand: true,
          discardSelector: ".discard-answer"
          ,immediatelyShowMarkdownHelp:true
          );



          );













          draft saved

          draft discarded


















          StackExchange.ready(
          function ()
          StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3157300%2freal-valued-vector-representation-of-hermitian-matrix%23new-answer', 'question_page');

          );

          Post as a guest















          Required, but never shown

























          0






          active

          oldest

          votes








          0






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes















          draft saved

          draft discarded
















































          Thanks for contributing an answer to Mathematics Stack Exchange!


          • Please be sure to answer the question. Provide details and share your research!

          But avoid


          • Asking for help, clarification, or responding to other answers.

          • Making statements based on opinion; back them up with references or personal experience.

          Use MathJax to format equations. MathJax reference.


          To learn more, see our tips on writing great answers.




          draft saved


          draft discarded














          StackExchange.ready(
          function ()
          StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3157300%2freal-valued-vector-representation-of-hermitian-matrix%23new-answer', 'question_page');

          );

          Post as a guest















          Required, but never shown





















































          Required, but never shown














          Required, but never shown












          Required, but never shown







          Required, but never shown

































          Required, but never shown














          Required, but never shown












          Required, but never shown







          Required, but never shown







          Popular posts from this blog

          How should I support this large drywall patch? Planned maintenance scheduled April 23, 2019 at 00:00UTC (8:00pm US/Eastern) Announcing the arrival of Valued Associate #679: Cesar Manara Unicorn Meta Zoo #1: Why another podcast?How do I cover large gaps in drywall?How do I keep drywall around a patch from crumbling?Can I glue a second layer of drywall?How to patch long strip on drywall?Large drywall patch: how to avoid bulging seams?Drywall Mesh Patch vs. Bulge? To remove or not to remove?How to fix this drywall job?Prep drywall before backsplashWhat's the best way to fix this horrible drywall patch job?Drywall patching using 3M Patch Plus Primer

          random experiment with two different functions on unit interval Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 23, 2019 at 00:00UTC (8:00pm US/Eastern)Random variable and probability space notionsRandom Walk with EdgesFinding functions where the increase over a random interval is Poisson distributedNumber of days until dayCan an observed event in fact be of zero probability?Unit random processmodels of coins and uniform distributionHow to get the number of successes given $n$ trials , probability $P$ and a random variable $X$Absorbing Markov chain in a computer. Is “almost every” turned into always convergence in computer executions?Stopped random walk is not uniformly integrable

          Lowndes Grove History Architecture References Navigation menu32°48′6″N 79°57′58″W / 32.80167°N 79.96611°W / 32.80167; -79.9661132°48′6″N 79°57′58″W / 32.80167°N 79.96611°W / 32.80167; -79.9661178002500"National Register Information System"Historic houses of South Carolina"Lowndes Grove""+32° 48' 6.00", −79° 57' 58.00""Lowndes Grove, Charleston County (260 St. Margaret St., Charleston)""Lowndes Grove"The Charleston ExpositionIt Happened in South Carolina"Lowndes Grove (House), Saint Margaret Street & Sixth Avenue, Charleston, Charleston County, SC(Photographs)"Plantations of the Carolina Low Countrye