Linear independence of symmetric matrix [on hold]












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If a symmetric matrix consists of pairwise linear independent vectors, does then follow that all vectors are linear independent, or can you give a counter example?






linear-algebra symmetric-matrices







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If a symmetric matrix consists of pairwise linear independent vectors, does then follow that all vectors are linear independent, or can you give a counter example?






linear-algebra symmetric-matrices







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put on hold as off-topic by user21820, Xander Henderson, rschwieb, quid♦ 9 hours ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – user21820, Xander Henderson, rschwieb, quid

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$begingroup$


If a symmetric matrix consists of pairwise linear independent vectors, does then follow that all vectors are linear independent, or can you give a counter example?






linear-algebra symmetric-matrices







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If a symmetric matrix consists of pairwise linear independent vectors, does then follow that all vectors are linear independent, or can you give a counter example?






linear-algebra symmetric-matrices




linear-algebra symmetric-matrices






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Thorben is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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asked 12 hours ago









ThorbenThorben

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put on hold as off-topic by user21820, Xander Henderson, rschwieb, quid♦ 9 hours ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – user21820, Xander Henderson, rschwieb, quid

If this question can be reworded to fit the rules in the help center, please edit the question.







put on hold as off-topic by user21820, Xander Henderson, rschwieb, quid♦ 9 hours ago


This question appears to be off-topic. The users who voted to close gave this specific reason:


  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – user21820, Xander Henderson, rschwieb, quid

If this question can be reworded to fit the rules in the help center, please edit the question.












  • $begingroup$
    Welcome to the site. Please explain via an edit what the context of this question is. The links in the box above give more explanation what is meant by "context";
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    – quid♦
    9 hours ago




















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    Welcome to the site. Please explain via an edit what the context of this question is. The links in the box above give more explanation what is meant by "context";
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    9 hours ago


















$begingroup$
Welcome to the site. Please explain via an edit what the context of this question is. The links in the box above give more explanation what is meant by "context";
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– quid♦
9 hours ago






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1 Answer
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How about $$begin{bmatrix}1&1&0\1&0&1\0&1&-1end{bmatrix}$$ the middle column is the first column minus the third.






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    1 Answer
    1






    active

    oldest

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    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

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    active

    oldest

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    8












    $begingroup$

    How about $$begin{bmatrix}1&1&0\1&0&1\0&1&-1end{bmatrix}$$ the middle column is the first column minus the third.






    share|cite|improve this answer









    $endgroup$


















      8












      $begingroup$

      How about $$begin{bmatrix}1&1&0\1&0&1\0&1&-1end{bmatrix}$$ the middle column is the first column minus the third.






      share|cite|improve this answer









      $endgroup$
















        8












        8








        8





        $begingroup$

        How about $$begin{bmatrix}1&1&0\1&0&1\0&1&-1end{bmatrix}$$ the middle column is the first column minus the third.






        share|cite|improve this answer









        $endgroup$



        How about $$begin{bmatrix}1&1&0\1&0&1\0&1&-1end{bmatrix}$$ the middle column is the first column minus the third.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered 11 hours ago









        DaveDave

        9,19111033




        9,19111033















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