How to calculate rank of 2 by 1 matrix..?

  1. how to calculate rank of 2 by 1 matrix..??

    hey guys so i am well familiar with finding out rank of square matrices but if matrix is just a row or column vector then how to determine its rank..considering the example below:
    a=[x1
    x2
    x3]
    where is column matrix while x1,x2,x3 are elements of this matrix..!!
     
  2. jcsd
  3. mfb

    Staff: Mentor

    Re: how to calculate rank of 2 by 1 matrix..??

    Can you find the column rank (the number of independent columns)?
    This is the same as the rank of the matrix.
     
  4. Re: how to calculate rank of 2 by 1 matrix..??

    hi there
    infact i am quite asking about how to calculate the rank of a column or row matrix..??
    and here i have just taken the example of row matrix..but i would also like to know about determining rank of a column matrix..!!
     
  5. HallsofIvy

    HallsofIvy 40,386
    Staff Emeritus
    Science Advisor

    Re: how to calculate rank of 2 by 1 matrix..??

    Any "n by 1" or "1 by n" matrix has rank "n".
     
  6. mfb

    Staff: Mentor

    Re: how to calculate rank of 2 by 1 matrix..??

    And I posted a hint.

    It has rank 1, if at least one entry is non-zero, and 0 otherwise. But never n, unless n=1.
     
  7. Re: how to calculate rank of 2 by 1 matrix..??

    ok..but here you have mentioned about column rank...but i am asking here is a different thing..i am asking about how to find the rank of column matrix or column vector i should say..!!
     
  8. mfb

    Staff: Mentor

    Re: how to calculate rank of 2 by 1 matrix..??

    It is not a different thing.
    Can you find the column rank of a column matrix? It is easy, and the answer was already posted here. The same applies to a row matrix and the row rank.
     
  9. Re: how to calculate rank of 2 by 1 matrix..??

    ok so can i say that any n by 1 or 1 by n matrix has rank of 1 ..!!
    but what if the independent rows or row vectors and columns or column vectors have value more than 1 like i have an example as:-
    x1=(1,3,4,2)
    x2=(3,-5,2,2)
    x3=(2,-1,3,2)
    so here i have three vetors x1,x2,x3 out of which two are independent x1,x2 while x3 is dependent as x3=(x1+x2)/2;
    and they all form a column matrix of 3 by 1 as
    A=[ x1
    x2
    x3 ]
    now acc to rule n by 1 and 1 by n we have rank 1 but checking independent rows as 2
    so what should be rank 1 or 2..??
     
  10. mfb

    Staff: Mentor

    Re: how to calculate rank of 2 by 1 matrix..??

    2. I don't see any reason why you would expect 1. It is a 3x4-matrix, this is neither nx1 nor 1xn.
     
  11. Re: how to calculate rank of 2 by 1 matrix..??

    now i am feeling stupid..!! i have been looking all along in terms of an individual vectors and not in terms of components ..!!
    thanks..:)
     
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