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Notation row/column of matrix.

  1. Nov 1, 2012 #1
    Is there notation to denote the i-th row of a Matrix or j-th column?
     
  2. jcsd
  3. Nov 1, 2012 #2

    Simon Bridge

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    Yes - several. What was the context?
    http://en.wikipedia.org/wiki/Matrix_(mathematics)#Notation

    eg. if ##a_{i,j}## denotes the i/jth element of ##\mathbf{A}## then ##a_{i,*}## is a common way to denote the ith row of ##\mathbf{A}##... or maybe the rows and columns would be represented as vectors.
     
    Last edited: Nov 1, 2012
  4. Nov 2, 2012 #3
    For example in a proof I would like to say:

    [itex]\exists i [/itex] such that the i-th column of A = the j-th row of B, basically i'm looking for the notation of i-th column, and j-th row.
     
  5. Nov 2, 2012 #4
    I sometimes use the notation [itex]A_{\bullet i}[/itex] to denote the i-th column and [itex]A_{j\bullet}[/itex] to denote the j-th row.
     
  6. Nov 2, 2012 #5
    Is there a standard for notation?
     
  7. Nov 2, 2012 #6

    Simon Bridge

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    No - as the wikipedia article (see link above) points out there is no standard (i.e. ISO standard) notation. Some journals may specify a particular form in their style guides. afaik the main ISO standard for matrix notation specifies bold-face (poss bf-italics).

    Per your example: one would most commonly write something like:$$\mathbf{A},\mathbf{B}\in \mathbb{M}_{m\times n}; a_{i,j}\in \mathbf{A}, b_{i,j}\in \mathbf{B}: a_{i,*}=b_{*,i}$$... and be fairly confident of being understood to mean that the ith row of A is the same as the ith column of B (pretty much the transpose but a fair example and you can have different functions of the row/column numbers.)
     
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