Chris,
  I think that you really need to quantify what you mean by correlation. 
Things to consider would depend on what the matrices represent--are they 
the estimates of the same set of N geographic points, are they traces of 
the same line, are they traces of the same polygon outline? If either of 
the latter two, then there would be no reason to believe that they had the 
same number of points. But the answer to the specific question would 
dictate how the correlation was computed.
Dave

below extracted from R-help Digest, Vol 111, Issue 7

Date: Sun, 6 May 2012 08:42:54 -0400
From: Sarah Goslee <sarah.goslee@gmail.com>
To: Christopher Kurby <kurbyc@gvsu.edu>
Cc: "r-help@r-project.org" <r-help@r-project.org>
Subject: Re: [R] correlation between XY coordinates
Message-ID: <4A58B3C4-C5B6-4C22-A7D3-BD79B8C1F0DA@gmail.com>
Content-Type: text/plain;   charset=us-ascii

Hi Chris,

To get a single value you might need something like a Mantel test, 
available in both ecodist and vegan. That test is a permutation test of 
significance of the correlation between two distance matrices.

Sarah

On May 6, 2012, at 8:06 AM, Christopher Kurby <kurbyc@gvsu.edu> wrote:

> Hey Josh (and everyone),
> 
> My apologies, let me be more specific. I have two sets of XY coordinates 
in Cartesian space. I would like to compute a correlation between the two 
sets. For example, let's say I have two N X 2 matrices, with the first 
column being the X coordinate, the second column being the Y, and with 
each row being a new observation. I would like to know the strength the 
relationship between the two sets of coordinates (matrices). cancor 
provides two separate correlations, but I want a single value representing 
the strength of the relationship. Is this more clear?
> 
> Chris
> 
> On May 5, 2012, at 11:44 PM, Joshua Wiley wrote:
> 
>> Hi Chris,
>> 
>> As Jeff mentioned, it is hard to tell what you want (correlations
>> between sets of coordinates could mean many things it seems like to
>> me), but here is something that perhaps helps:
>> 
>> ## some data (usually nice if you provide this rather than us having
>> to make something up)
>> d1 <- cbind(x <- rnorm(100), y <- rnorm(100))
>> d2 <- cbind(x2 = x + rnorm(100), y2 = y + rnorm(100))
>> 
>> ## canonical correlation of the two matrices
>> cancor(d1, d2)
>> 
>> ## simple correlation matrix of each dataset
>> cor(d1)
>> cor(d2)
>> 
>> Cheers,
>> 
>> Josh
>> 
>> On Sat, May 5, 2012 at 5:32 PM, Christopher Kurby <kurbyc@gvsu.edu> 
wrote:
>>> Hello r world,
>>> 
>>> Does anyone know a function or package that can compute correlations 
between sets of XY coordinates?
>>> 
>>> Thanks in advance for your help,
>>> Chris
>>> 
>>> ______________________________________________
>>> R-help@r-project.org mailing list
>>> https://stat.ethz.ch/mailman/listinfo/r-help
>>> PLEASE do read the posting guide 
http://www.R-project.org/posting-guide.html
>>> and provide commented, minimal, self-contained, reproducible code.
>> 
>> 
>> 
>> -- 
>> Joshua Wiley
>> Ph.D. Student, Health Psychology
>> Programmer Analyst II, Statistical Consulting Group
>> University of California, Los Angeles
>> https://joshuawiley.com/
> 
> ______________________________________________
> R-help@r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide 
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.


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