some confusion in upper traingular matrix?











up vote
1
down vote

favorite












$1$. What is the dimension of the subspace of all real $n times n$ matrix of upper triangular matrix?



$2$. What is dimension of all real $n times n$ matrix of upper triangular ?



Is both option



$1)$



and



$2)$ having same dimension?



Any hints/solution






linear-algebra







share|cite|improve this question




























    up vote
    1
    down vote

    favorite












    $1$. What is the dimension of the subspace of all real $n times n$ matrix of upper triangular matrix?



    $2$. What is dimension of all real $n times n$ matrix of upper triangular ?



    Is both option



    $1)$



    and



    $2)$ having same dimension?



    Any hints/solution






    linear-algebra







    share|cite|improve this question


























      up vote
      1
      down vote

      favorite









      up vote
      1
      down vote

      favorite











      $1$. What is the dimension of the subspace of all real $n times n$ matrix of upper triangular matrix?



      $2$. What is dimension of all real $n times n$ matrix of upper triangular ?



      Is both option



      $1)$



      and



      $2)$ having same dimension?



      Any hints/solution






      linear-algebra







      share|cite|improve this question















      $1$. What is the dimension of the subspace of all real $n times n$ matrix of upper triangular matrix?



      $2$. What is dimension of all real $n times n$ matrix of upper triangular ?



      Is both option



      $1)$



      and



      $2)$ having same dimension?



      Any hints/solution






      linear-algebra




      linear-algebra






      share|cite|improve this question















      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited Nov 27 at 15:35









      amWhy

      191k28223439




      191k28223439










      asked Nov 27 at 14:07









      Messi fifa

      50111




      50111






















          2 Answers
          2






          active

          oldest

          votes

















          up vote
          2
          down vote



          accepted










          For 2), let be $S$ the space of upper triangular matrix $M_n(R)$. So the dimension is equal to the elements in that space that can be a base (every matrix with 1 in any single place) so the dimension will be dim($S$)$= n+(n-1)+(n-2)+...+3+2+1 = {n(n+1) over 2 }$; of course it depends on $n$.



          For sure dim($S$) < $n*n$ in this case.
          Every element of this kind can be a base remember!



          For 1), is the same as 2), the "subspace" requirements seems identical to question 2).






          share|cite|improve this answer





















          • .@alessar .is this method same for lower triangular ??
            – Messi fifa
            Nov 27 at 14:24








          • 1




            The matrix is $n*n$, so the dimension is the same; they are simply symmetrical respect the principal diagonal
            – Alessar
            Nov 27 at 14:26








          • 1




            thanks u got its
            – Messi fifa
            Nov 27 at 14:28


















          up vote
          2
          down vote













          HINT



          An upper triangular matrix is defined by $N=frac{n(n+1)}{2}$ elements.






          share|cite|improve this answer





















            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',
            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%2f3015810%2fsome-confusion-in-upper-traingular-matrix%23new-answer', 'question_page');
            }
            );

            Post as a guest















            Required, but never shown

























            2 Answers
            2






            active

            oldest

            votes








            2 Answers
            2






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes








            up vote
            2
            down vote



            accepted










            For 2), let be $S$ the space of upper triangular matrix $M_n(R)$. So the dimension is equal to the elements in that space that can be a base (every matrix with 1 in any single place) so the dimension will be dim($S$)$= n+(n-1)+(n-2)+...+3+2+1 = {n(n+1) over 2 }$; of course it depends on $n$.



            For sure dim($S$) < $n*n$ in this case.
            Every element of this kind can be a base remember!



            For 1), is the same as 2), the "subspace" requirements seems identical to question 2).






            share|cite|improve this answer





















            • .@alessar .is this method same for lower triangular ??
              – Messi fifa
              Nov 27 at 14:24








            • 1




              The matrix is $n*n$, so the dimension is the same; they are simply symmetrical respect the principal diagonal
              – Alessar
              Nov 27 at 14:26








            • 1




              thanks u got its
              – Messi fifa
              Nov 27 at 14:28















            up vote
            2
            down vote



            accepted










            For 2), let be $S$ the space of upper triangular matrix $M_n(R)$. So the dimension is equal to the elements in that space that can be a base (every matrix with 1 in any single place) so the dimension will be dim($S$)$= n+(n-1)+(n-2)+...+3+2+1 = {n(n+1) over 2 }$; of course it depends on $n$.



            For sure dim($S$) < $n*n$ in this case.
            Every element of this kind can be a base remember!



            For 1), is the same as 2), the "subspace" requirements seems identical to question 2).






            share|cite|improve this answer





















            • .@alessar .is this method same for lower triangular ??
              – Messi fifa
              Nov 27 at 14:24








            • 1




              The matrix is $n*n$, so the dimension is the same; they are simply symmetrical respect the principal diagonal
              – Alessar
              Nov 27 at 14:26








            • 1




              thanks u got its
              – Messi fifa
              Nov 27 at 14:28













            up vote
            2
            down vote



            accepted







            up vote
            2
            down vote



            accepted






            For 2), let be $S$ the space of upper triangular matrix $M_n(R)$. So the dimension is equal to the elements in that space that can be a base (every matrix with 1 in any single place) so the dimension will be dim($S$)$= n+(n-1)+(n-2)+...+3+2+1 = {n(n+1) over 2 }$; of course it depends on $n$.



            For sure dim($S$) < $n*n$ in this case.
            Every element of this kind can be a base remember!



            For 1), is the same as 2), the "subspace" requirements seems identical to question 2).






            share|cite|improve this answer












            For 2), let be $S$ the space of upper triangular matrix $M_n(R)$. So the dimension is equal to the elements in that space that can be a base (every matrix with 1 in any single place) so the dimension will be dim($S$)$= n+(n-1)+(n-2)+...+3+2+1 = {n(n+1) over 2 }$; of course it depends on $n$.



            For sure dim($S$) < $n*n$ in this case.
            Every element of this kind can be a base remember!



            For 1), is the same as 2), the "subspace" requirements seems identical to question 2).







            share|cite|improve this answer












            share|cite|improve this answer



            share|cite|improve this answer










            answered Nov 27 at 14:18









            Alessar

            17213




            17213












            • .@alessar .is this method same for lower triangular ??
              – Messi fifa
              Nov 27 at 14:24








            • 1




              The matrix is $n*n$, so the dimension is the same; they are simply symmetrical respect the principal diagonal
              – Alessar
              Nov 27 at 14:26








            • 1




              thanks u got its
              – Messi fifa
              Nov 27 at 14:28


















            • .@alessar .is this method same for lower triangular ??
              – Messi fifa
              Nov 27 at 14:24








            • 1




              The matrix is $n*n$, so the dimension is the same; they are simply symmetrical respect the principal diagonal
              – Alessar
              Nov 27 at 14:26








            • 1




              thanks u got its
              – Messi fifa
              Nov 27 at 14:28
















            .@alessar .is this method same for lower triangular ??
            – Messi fifa
            Nov 27 at 14:24






            .@alessar .is this method same for lower triangular ??
            – Messi fifa
            Nov 27 at 14:24






            1




            1




            The matrix is $n*n$, so the dimension is the same; they are simply symmetrical respect the principal diagonal
            – Alessar
            Nov 27 at 14:26






            The matrix is $n*n$, so the dimension is the same; they are simply symmetrical respect the principal diagonal
            – Alessar
            Nov 27 at 14:26






            1




            1




            thanks u got its
            – Messi fifa
            Nov 27 at 14:28




            thanks u got its
            – Messi fifa
            Nov 27 at 14:28










            up vote
            2
            down vote













            HINT



            An upper triangular matrix is defined by $N=frac{n(n+1)}{2}$ elements.






            share|cite|improve this answer

























              up vote
              2
              down vote













              HINT



              An upper triangular matrix is defined by $N=frac{n(n+1)}{2}$ elements.






              share|cite|improve this answer























                up vote
                2
                down vote










                up vote
                2
                down vote









                HINT



                An upper triangular matrix is defined by $N=frac{n(n+1)}{2}$ elements.






                share|cite|improve this answer












                HINT



                An upper triangular matrix is defined by $N=frac{n(n+1)}{2}$ elements.







                share|cite|improve this answer












                share|cite|improve this answer



                share|cite|improve this answer










                answered Nov 27 at 14:19









                gimusi

                91.9k84495




                91.9k84495






























                    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.





                    Some of your past answers have not been well-received, and you're in danger of being blocked from answering.


                    Please pay close attention to the following guidance:


                    • 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.


                    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%2f3015810%2fsome-confusion-in-upper-traingular-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

                    Berounka

                    Image
                    Berounka.mw-parser-output .entete.map{background-image:url("//upload.wikimedia.org/wikipedia/commons/7/7a/Picto_infobox_map.png")} Caractéristiques Longueur 139  km Bassin 8 861  km 2 Bassin collecteur Elbe Débit moyen ? Cours Source Confluence de la Mže et de la Radbuza · Localisation Pilsen · Altitude 305  m · Coordonnées 49° 45′ 13″ N, 13° 23′ 24″ E Confluence Vltava · Localisation Prague · Altitude 187  m · Coordonnées 49° 59′ 43″ N, 14° 24′ 04″ E Géographie Pays traversés   République tchèque modifier   La Berounka est une rivière de la République tchèque. Elle porte le nom de Mže depuis sa source en Allemagne près de la frontière jusqu'à sa confluence avec la Radbuza à Plzeň. Elle continue ensuite sous le nom de Berounka jusqu'à sa confluence avec la Vltava, près de Prague. La rivière est une destination prisée pour les amateurs de canoë, qui appréc...
                    Read more

                    Sphinx de Gizeh

                    Image
                    Pour les articles homonymes, voir Sphinx. Sphinx de Gizeh.mw-parser-output .entete.egypte-antique{background-image:url("//upload.wikimedia.org/wikipedia/commons/c/cc/Picto_infobox_ancient_Egypt.png")} Site d'Égypte antique Le visage du sphinx de Gizeh. Noms en arabe أبو الهول , Abou al-Hôl Localisation Région Basse-Égypte Coordonnées 29° 58′ 31″ nord, 31° 08′ 16″ est Géolocalisation sur la carte : Égypte Sphinx de Gizeh modifier   Le sphinx de Gizeh est la statue thérianthrope qui se dresse devant les grandes pyramides du plateau de Gizeh, en Basse-Égypte. Sculpture monumentale monolithique la plus grande du monde [ 1 ] avec 73,5 mètres de longueur, 14 mètres de largeur et 20,22 mètres de hauteur, elle représente un sphinx couchant. Réalisée vers -2500, elle serait attribuée à Djédefrê, l'un des pharaons de la IV e  dynastie, représentant son père le pharaon Khéops. Sommaire 1 Étymologie 2 Desc...
                    Read more

                    Different font size/position of beamer's navigation symbols template's content depending on regular/plain...

                    Image
                    3 Let's suppose I'd like to divert the navigation symbols template (e.g. in order replace them by the frame numbers, see this bug report ;) I would be facing troubles regarding the font size/position, depending on regular/plain frames, as shown by the following MCE. How could I get rid of these troubles? documentclass{beamer} usetheme{PaloAlto} setbeamertemplate{navigation symbols}{insertframenumber/inserttotalframenumber} begin{document} begin{frame} frametitle{A regular frame} end{frame} begin{frame}[plain] frametitle{A plain frame} end{frame} end{document} beamer header-footer share | improve this question asked Dec 10 '18 a...
                    Read more