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.}

**Follow-Ups**:**Re: How Functions are Applied to Matrices***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>