# Submatrix Notation

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.

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In Matlab/Octave, the notation $a(1:3,2:4)$ means select the submatrix consisting of rows 1-3, and columns 2-4. –  copper.hat Jul 29 '12 at 17:08
If it helps, the paper I'm looking at is cs.ust.hk/mjg_lib/bibs/DPSu/DPSu.Files/Wi88.PDF –  OmnipotentEntity Jul 29 '12 at 17:11
Look at p.422 where they define the notation midway down the page. –  copper.hat Jul 29 '12 at 17:23
Thank you very much. –  OmnipotentEntity Jul 29 '12 at 17:41