Re: mathematica newbie question

*To*: mathgroup at smc.vnet.net*Subject*: [mg66912] Re: mathematica newbie question*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>*Date*: Sat, 3 Jun 2006 03:26:19 -0400 (EDT)*Organization*: The Open University, Milton Keynes, UK*References*: <e5osv8$i51$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Jeremy Watts wrote: > Hi, > > Just trying to get to grips with Mathematica and matrices. Why is it when I > enter :- > {0, 0, 0}, {1, -1, -1}, {-1, 1, 1}}^2 > > then Mathematica returns :- > > {{0, 0, 0}, {1, 1, 1}, {1, 1, 1}} > > and not {{0,0,0},{0,0,0},{0,0,0}} (the actual square of the matrix) as I'd > have expected? > > Is it treating what I entered as separate vectors or something, and not an > actual matrix? Hi Jeremy, Mathematica knows nothing about "matrices" per se. Well, this statement is slightly extreme; but the fact is that, to Mathematica, a list of lists is first a list of lists that can contains lists of different lengths, each of them holding elements of different types. For instance, the following list is a valid construct in Mathematica {{a,b,c},{"Some string",{1,2,{3,4},index}},{Sin,Cos}} Of course, this expression cannot be interpreted as a matrix. On the other hand, your original expression -- called "mat" in the remaining of this post, see In[1] -- can be interpreted as a matrix since, say, taking the dot product of a 3 by 3 structure of integers makes sense (see In[4]). However, mat is still a regular expression and Mathematica can works on it element by element (see In[2] and In[3]). Therefore, to get raise a matrix to a power, either use repeatedly the dot product or use special built-in functions such as MatrixExp or MatrixPower (see In[4] and In[5]). Finally, the article "Functions of Matrices" [1] may be of interest. In[1]:= mat = {{0, 0, 0}, {1, -1, -1}, {-1, 1, 1}}; In[2]:= mat^2 Out[2]= {{0, 0, 0}, {1, 1, 1}, {1, 1, 1}} In[3]:= mat*mat Out[3]= {{0, 0, 0}, {1, 1, 1}, {1, 1, 1}} In[4]:= mat . mat Out[4]= {{0, 0, 0}, {0, 0, 0}, {0, 0, 0}} In[5]:= MatrixPower[mat, 2] Out[5]= {{0, 0, 0}, {0, 0, 0}, {0, 0, 0}} HTH, Jean-Marc [1] http://documents.wolfram.com/mathematica/Built-inFunctions/AdvancedDocumentation/LinearAlgebra/LinearAlgebraInMathematica/MatrixComputations/AdvancedDocumentationLinearAlgebra3.5.html