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I'm looking through some computer science papers and I see some notation that I'm just not familiar with.

Consider an 5 x 6 matrix

$$G = \begin{pmatrix} a_{0,0} & a_{0,1} & a_{0,2} & a_{0,3} & a_{0,4} & a_{0,5} \\ a_{1,0} & a_{1,1} & a_{1,2} & a_{1,3} & a_{1,4} & a_{1,5} \\ a_{2,0} & a_{2,1} & a_{2,2} & a_{2,3} & a_{2,4} & a_{2,5} \\ a_{3,0} & a_{3,1} & a_{3,2} & a_{3,3} & a_{3,4} & a_{3,5} \\ a_{4,0} & a_{4,1} & a_{4,2} & a_{4,3} & a_{4,4} & a_{4,5} \\ \end{pmatrix}$$

If I wrote down $G[1,3; 2,5]$ does that mean row 1 to row3 inclusive and col 2 to col 5 inclusive:

$$G[1,3; 2,5] = \begin{pmatrix} a_{0,1} & a_{0,2} & a_{0,3} & a_{0,4} \\ a_{1,1} & a_{1,2} & a_{1,3} & a_{1,4} \\ a_{2,1} & a_{2,2} & a_{2,3} & a_{2,4} \\ \end{pmatrix}$$

Or (zero indexed version of previous):

$$G[1,3; 2,5] = \begin{pmatrix} a_{1,2} & a_{1,3} & a_{1,4} & a_{1,5} \\ a_{2,2} & a_{2,3} & a_{2,4} & a_{2,5} \\ a_{3,2} & a_{3,3} & a_{3,4} & a_{3,5} \\ \end{pmatrix}$$

Or the rectangle made by the element at row 1 col 3 to the element at row 2 col 5:

$$G[1,3; 2,5] = \begin{pmatrix} a_{0,2} & a_{0,3} & a_{0,4} \\ a_{1,2} & a_{1,3} & a_{1,4} \\ \end{pmatrix}$$

Or (zero indexed version of previous):

$$G[1,3; 2,5] = \begin{pmatrix} a_{1,3} & a_{1,4} & a_{1,5} \\ a_{2,3} & a_{2,4} & a_{2,5} \\ \end{pmatrix}$$

Or the intersection of rows 1 and 3 with the intersection of rows 2 and 5:

$$G[1,3; 2,5] = \begin{pmatrix} a_{0,1} & a_{0,4} \\ a_{2,1} & a_{2,4} \\ \end{pmatrix}$$

Or (zero indexed version of previous):

$$G[1,3; 2,5] = \begin{pmatrix} a_{1,2} & a_{1,5} \\ a_{3,2} & a_{3,5} \\ \end{pmatrix}$$

Or the same thing but specified row, col; row, col (like possibility 3 and 4)

$$G[1,3; 2,5] = \begin{pmatrix} a_{0,2} & a_{0,4} \\ a_{1,2} & a_{1,4} \\ \end{pmatrix}$$

Or (zero indexed version):

$$G[1,3; 2,5] = \begin{pmatrix} a_{1,3} & a_{1,5} \\ a_{2,3} & a_{2,5} \\ \end{pmatrix}$$

Sorry, if this is a rather elementary question, I was simply unfamiliar with the notation and I couldn't find any information on the Internet about it.

  • 0
    In Matlab/Octave, the notation $a(1:3,2:4)$ means select the submatrix consisting of rows 1-3, and columns 2-4.2012-07-29
  • 0
    If it helps, the paper I'm looking at is http://www.cs.ust.hk/mjg_lib/bibs/DPSu/DPSu.Files/Wi88.PDF2012-07-29
  • 6
    Look at p.422 where they define the notation midway down the page.2012-07-29

0 Answers 0