矩阵运算
论numpy中matrix 和 array的区别：
http://blog.csdn.net/vincentlipan/article/details/20717163
matrix 和 array的差别： Numpy matrices必须是2维的,但是 numpy arrays (ndarrays) 可以是多维的（1D，2D，3D····ND）. Matrix是Array的一个小的分支，包含于Array。所以matrix 拥有array的所有特性。
1.基本运算
import numpy as np
a = np.array([[-1,2],[2,3]])
b = np.array([[3,4],[4,5]])
print '\n a:\n',a
print '\n b:\n',b
##转置
print '\n a transpose:\n',a.T
##共扼矩阵
#print '\n a H:\n',a.I
##逆矩阵
print '\n a inv:\n',np.linalg.inv(a) # 求逆
##转置
print '\n a transpose:\n',a.T
# a + b，矩阵相加
print "\n a+b: \n",a+b
# a - b，矩阵相减
print "\n a-b: \n",a-b
#2x2 矩阵，矩阵相乘
print "\n a mul b:\n",a.dot(b.T)
#2x3矩阵，矩阵点乘
print "\n a dot b: \n",a*b
#2x3矩阵，矩阵点除
print "\n a/b \n:",a/np.linalg.inv(b)
#求迹
print "\n a trace",np.trace(a)
#特征，特征向量
eigval,eigvec = np.linalg.eig(a)
#eigval = np.linalg.eigvals(a) #直接求解特征值
print "\n a eig value:\n",eigval,
print'\n a eig vector:\n',eigvec运算结果：
a:
[[-1 2]
[ 2 3]]
b:
[[3 4]
[4 5]]
a transpose:
[[-1 2]
[ 2 3]]
a inv:
[[-0.42857143 0.28571429]
[ 0.28571429 0.14285714]]
a transpose:
[[-1 2]
[ 2 3]]
a+b:
[[2 6]
[6 8]]
a-b:
[[-4 -2]
[-2 -2]]
a mul b:
[[ 5 6]
[18 23]]
a dot b:
[[-3 8]
[ 8 15]]
a/b
: [[ 0.2 0.5]
[ 0.5 -1. ]]
a trace 2
a eig value:
[-1.82842712 3.82842712]
a eig vector:
[[-0.92387953 -0.38268343]
[ 0.38268343 -0.92387953]]2.特殊矩阵
import numpy as np
a = np.zeros([4,5]) # all zero
print '\nall zero \n',a
a = np.ones([7,6]) # all one
print '\nall one \n',a
a = np.eye(4,7) # 4x7 diagonal
print '\n4x7 diagonal \n',a
a = np.diag(range(5)) # 5x5 diagonal
print '\n5x5 diagonal \n',a
a = np.empty((2,3))
print '\nempty \n',a
a = np.arange(10, 30, 5) # array([10, 15, 20, 25]), 1-D
print '\n array([10, 15, 20, 25]), 1-D \n',a
a = np.linspace(0, 2, 9) # 9 numbers from 0 to 2
print '\n9 numbers from 0 to 2 \n',a
a = np.random.random((2,3)) # random matrics
print '\nrandom matrics \n',a
import numpy as np
a = np.zeros([4,5]) # all zero
print '\nall zero \n',a
a = np.ones([7,6]) # all one
print '\nall one \n',a
a = np.eye(4,7) # 4x7 diagonal
print '\n4x7 diagonal \n',a
a = np.diag(range(5)) # 5x5 diagonal
print '\n5x5 diagonal \n',a
a = np.empty((2,3))
print '\nempty \n',a
a = np.arange(10, 30, 5) # array([10, 15, 20, 25]), 1-D
print '\n array([10, 15, 20, 25]), 1-D \n',a
a = np.linspace(0, 2, 9) # 9 numbers from 0 to 2
print '\n9 numbers from 0 to 2 \n',a
a = np.random.random((2,3)) # random matrics
print '\nrandom matrics \n',a运算结果：
all zero
[[ 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0.]
[ 0. 0. 0. 0. 0.]]
all one
[[ 1. 1. 1. 1. 1. 1.]
[ 1. 1. 1. 1. 1. 1.]
[ 1. 1. 1. 1. 1. 1.]
[ 1. 1. 1. 1. 1. 1.]
[ 1. 1. 1. 1. 1. 1.]
[ 1. 1. 1. 1. 1. 1.]
[ 1. 1. 1. 1. 1. 1.]]
4x7 diagonal
[[ 1. 0. 0. 0. 0. 0. 0.]
[ 0. 1. 0. 0. 0. 0. 0.]
[ 0. 0. 1. 0. 0. 0. 0.]
[ 0. 0. 0. 1. 0. 0. 0.]]
5x5 diagonal
[[0 0 0 0 0]
[0 1 0 0 0]
[0 0 2 0 0]
[0 0 0 3 0]
[0 0 0 0 4]]
empty
[[ 0.06012241 0.30847312 0.20174074]
[ 0.37654373 0.71036135 0.15586512]]
array([10, 15, 20, 25]), 1-D
[10 15 20 25]
numbers from 0 to 2
[ 0. 0.25 0.5 0.75 1. 1.25 1.5 1.75 2. ]
random matrics
[[ 0.44052293 0.42283564 0.44825331]
[ 0.66735609 0.32664018 0.17015328]]