# Why are Cartesian coordinates ordered x, y but matrix coordinates are ordered r, c?

Lets say I have the following plane:

 4
3
2
1
0 1 2 3 4
-1
-2
-3
-4


and a matrix like this:

-          -
|  1  2  3 |
|  4  5  6 |
|  7  8  9 |
| 10 11 12 |
-          -


When referring to the coordinates of the Cartesian plane (2, 3), we move left to right using the first coordinate(2) and top to bottom with the second coordinate(3). But when referring to a matrix, we say the above is a 4 x 3 matrix where the first coordinate(4) follows the y-axis top to bottom and the second coordinate(3) follows the x-axis left to right. It seems counter-intuitive to reverse the way these structures are represented. I feel like Descartes' system is more intuitive but that may be because I learned that system first and, while I know matricies are an older concept, I was unable to determine the actual date of when the M x N coordinate system was first used. Is there a [good] reason that one notation is used one way in one place and the opposite in the other?

• I believe Descartes' system predates the idea of matrices. But good question nonetheless. – Servaes Oct 18 '18 at 20:25
• It’s quite common in computer graphics to have $y$ increasing downward on the screen/page. – amd Oct 18 '18 at 21:04
• According to this en.wikipedia.org/wiki/Matrix_(mathematics)#History matricies predate Descartes by more than a millennium. That's why I believe that. – user221909 Oct 19 '18 at 13:35