Like matlab, numpy and scipy have support for fast linear algebra
built upon the highly optimized LAPACK, BLAS and ATLAS fortran linear
algebra libraries. Unlike Matlab, in which everything is a matrix or
vector, and the '*' operator always means matrix multiple, the default
object in numpy is an \texttt{array}, and the '*' operator on arrays means
element-wise multiplication.
Instead, numpy provides a \texttt{matrix} class if you want to do
standard matrix-matrix multiplication with the '*' operator, or the
\texttt{dot} function if you want to do matrix multiplies with plain
arrays. The basic linear algebra functionality is found in
\texttt{numpy.linalg}
\begin{lstlisting}
In [1]: import numpy as npy
In [2]: import numpy.linalg as linalg
# X and Y are arrays
In [3]: X = npy.random.rand(3,3)
In [4]: Y = npy.random.rand(3,3)
# * operator is element wise multiplication, not matrix matrix
In [5]: print X*Y
[[ 0.00973215 0.18086148 0.05539387]
[ 0.00817516 0.63354021 0.2017993 ]
[ 0.34287698 0.25788149 0.15508982]]
# the dot function will use optimized LAPACK to do matrix-matix
# multiply
In [6]: print npy.dot(X, Y)
[[ 0.10670678 0.68340331 0.39236388]
[ 0.27840642 1.14561885 0.62192324]
[ 0.48192134 1.32314856 0.51188578]]
# the matrix class will create matrix objects that support matrix
# multiplication with *
In [7]: Xm = npy.matrix(X)
In [8]: Ym = npy.matrix(Y)
In [9]: print Xm*Ym
[[ 0.10670678 0.68340331 0.39236388]
[ 0.27840642 1.14561885 0.62192324]
[ 0.48192134 1.32314856 0.51188578]]
# the linalg module provides functions to compute eigenvalues,
# determinants, etc. See help(linalg) for more info
In [10]: print linalg.eigvals(X)
[ 1.46131600+0.j 0.46329211+0.16501143j 0.46329211-0.16501143j]
\end{lstlisting}
