Results 1 to 7 of 7

Math Help - a matrix that has zeroes everywhere except for one element - name

  1. #1
    Member
    Joined
    Feb 2011
    Posts
    147
    Thanks
    3

    a matrix that has zeroes everywhere except for one element - name

    Is there a name for a matrix that has zeroes everywhery except for one element? Is there a name for a matrix of this kind in which the nonzero element equals 1?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Also sprach Zarathustra's Avatar
    Joined
    Dec 2009
    From
    Russia
    Posts
    1,506
    Thanks
    1

    Re: a matrix that has zeroes everywhere except for one element - name

    Quote Originally Posted by ymar View Post
    Is there a name for a matrix that has zeroes everywhery except for one element? Is there a name for a matrix of this kind in which the nonzero element equals 1?
    I don't think so, but here is List of matrices - Wikipedia, the free encyclopedia
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Feb 2011
    Posts
    147
    Thanks
    3

    Re: a matrix that has zeroes everywhere except for one element - name

    Right, I've seen the list, but I couldn't find it there.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Mar 2011
    From
    Tejas
    Posts
    3,392
    Thanks
    759

    Re: a matrix that has zeroes everywhere except for one element - name

    sometimes these are called the elementary matrices Ei,j when the i,j-th entry is 1 and all other entries are 0. these form a basis for the vector space of all nxn matrices over a field.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,714
    Thanks
    1472

    Re: a matrix that has zeroes everywhere except for one element - name

    Those certainly do form a basis for the space of n by n matrices but that is not my understanding of "elementary matrix". An elementary matrix is one that is derived from the identity matrix by a single row operation.

    See definition 3 in Pauls Online Notes : Linear Algebra - Inverse Matrices and Elementary Matrices
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member
    Joined
    Feb 2011
    Posts
    147
    Thanks
    3

    Re: a matrix that has zeroes everywhere except for one element - name

    Quote Originally Posted by HallsofIvy View Post
    Those certainly do form a basis for the space of n by n matrices but that is not my understanding of "elementary matrix". An elementary matrix is one that is derived from the identity matrix by a single row operation.

    See definition 3 in Pauls Online Notes : Linear Algebra - Inverse Matrices and Elementary Matrices
    This is also the meaning of "elementary matrix" in know. Thank you both.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor

    Joined
    Mar 2011
    From
    Tejas
    Posts
    3,392
    Thanks
    759

    Re: a matrix that has zeroes everywhere except for one element - name

    Quote Originally Posted by HallsofIvy View Post
    Those certainly do form a basis for the space of n by n matrices but that is not my understanding of "elementary matrix". An elementary matrix is one that is derived from the identity matrix by a single row operation.

    See definition 3 in Pauls Online Notes : Linear Algebra - Inverse Matrices and Elementary Matrices
    yes, that is the more usual use of "elementary matrix", the matrix form of an elementary row-operation. that is why i said "sometimes"...

    if one wishes to identify M(mxn)(F) with F^(mn), then these are just the standard basis vectors of F^(mn) (well, the image under the inverse isomorphism of the standard basis-that's a mouthful).

    i didn't invent, or make up this usage: for example, see the footnote on page 6 here: http://www.colorado.edu/engineering/.../IFEM.AppD.pdf
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Orbits of an element and the Stabilizer of the element
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: December 24th 2011, 05:41 AM
  2. Matrix element of a field
    Posted in the Advanced Algebra Forum
    Replies: 8
    Last Post: September 25th 2011, 04:29 AM
  3. Replies: 9
    Last Post: October 9th 2010, 02:53 PM
  4. Replies: 3
    Last Post: March 23rd 2010, 07:05 PM
  5. Derivative of matrix element
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: February 27th 2010, 09:05 AM

Search Tags


/mathhelpforum @mathhelpforum