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MathGroup Archive 2006

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How Functions are Applied to Matrices

  • To: mathgroup at smc.vnet.net
  • Subject: [mg66064] How Functions are Applied to Matrices
  • From: Gregory Lypny <gregory.lypny at videotron.ca>
  • Date: Fri, 28 Apr 2006 06:32:58 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Hello everyone,

If I use functions, such as Mean, StandardDeviation, or Total, that  
operate on lists, they work the way I expect when applied to a single  
list.  So, for example, the mean of data[[2]] below is 5.25.   
However, when I apply Mean to the entire 3 x 4 matrix, which I  
understand to be three lists, I expect to get three means.  Instead I  
get four because Mean is operating on the columns and not the rows,  
that is, the four corresponding elements of each of the three lists.

Why is that?

	Greg


data={{-9,8,3,1},{2,12,3,4},{-6,-9,-9,8}}

The mean of the second list:

In[182]:=
Mean[data[[2]]]//N

Out[182]=
5.25

Applying Mean to the whole matrix computes the mean of columns, not  
rows.

In[181]:=
Mean[data]//N

Out[181]=
{-4.33333,3.66667,-1.,4.33333}

I need to Map it to have it applied to each list.

In[183]:=
Map[Mean,data]//N

Out[183]=
{0.75,5.25,-4.}


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