Numpy matrices必須是2維的,但是numpy arrays (ndarrays) 可以是多維的（1D，2D，3D····ND）. Matrix是Array的一個小的分支，包含于Array。所以matrix 擁有array的所有特性。

　　在numpy中matrix的主要優勢是：相對簡單的乘法運算符號。例如，a和b是兩個matrices，那么a*b，就是矩陣積。

　　import numpy as np

　　a=np.mat('4 3; 2 1')
　　b=np.mat('1 2; 3 4')
　　print(a)
　　# [[4 3]
　　# [2 1]]
　　print(b)
　　# [[1 2]
　　# [3 4]]
　　print(a*b)
　　# [[13 20]
　　# [ 5 8]]
　　matrix 和 array 都可以通過在have.Tto return the transpose, but matrix objects also have.Hfor the conjugate transpose, and.Ifor the inverse.

　　In contrast, numpy arrays consistently abide by the rule that operations are applied element-wise. Thus, if a and b are numpy arrays, then a*b is the array formed by multiplying the components element-wise:

　　c=np.array([[4, 3], [2, 1]])
　　d=np.array([[1, 2], [3, 4]])
　　print(c*d)
　　# [[4 6]
　　# [6 4]]
　　To obtain the result of matrix multiplication, you use np.dot :

　　print(np.dot(c,d))
　　# [[13 20]
　　# [ 5 8]]
　　The**operator also behaves differently:

　　print(a**2)
　　# [[22 15]
　　# [10 7]]
　　print(c**2)
　　# [[16 9]
　　# [ 4 1]]
　　Sinceais a matrix,a**2returns the matrix producta*a. Sincecis an ndarray,c**2returns an ndarray with each component squared element-wise.

　　There are other technical differences between matrix objects and ndarrays (having to do with np.ravel, item selection and sequence behavior).

　　The main advantage of numpy arrays is that they are more general than 2-dimensional matrices. What happens when you want a 3-dimensional array? Then you have to use an ndarray, not a matrix object. Thus, learning to use matrix objects is more work -- you have to learn matrix object operations, and ndarray operations.

　　Writing a program that uses both matrices and arrays makes your life difficult because you have to keep track of what type of object your variables are, lest multiplication return something you don't expect.

　　In contrast, if you stick solely with ndarrays, then you can do everything matrix objects can do, and more, except with slightly different functions/notation.

　　If you are willing to give up the visual appeal of numpy matrix product notation, then I think numpy arrays are definitely the way to go.

　　PS. Of course, you really don't have to choose one at the expense of the other, sincenp.asmatrixandnp.asarrayallow you to convert one to the other (as long as the array is 2-dimensional).

　　One of the biggest practical differences for me of numpy ndarrays compared to numpy matrices or matrix languages like matlab, is that the dimension is not preserved in reduce operations. Matrices are always 2d, while the mean of an array, for example, has one dimension less.

　　For example demean rows of a matrix or array:

　　with matrix

　　>>> m = np.mat([[1,2],[2,3]])
　　>>> m
　　matrix([[1, 2],
　　[2, 3]])
　　>>> mm = m.mean(1)
　　>>> mm
　　matrix([[ 1.5],
　　[ 2.5]])
　　>>> mm.shape
　　(2, 1)
　　>>> m - mm
　　matrix([[-0.5, 0.5],
　　[-0.5, 0.5]])
　　with array

　　>>> a = np.array([[1,2],[2,3]])
　　>>> a
　　array([[1, 2],
　　[2, 3]])
　　>>> am = a.mean(1)
　　>>> am.shape
　　(2,)
　　>>> am
　　array([ 1.5, 2.5])
　　>>> a - am #wrong
　　array([[-0.5, -0.5],
　　[ 0.5, 0.5]])
　　>>> a - am[:, np.newaxis] #right
　　array([[-0.5, 0.5],
　　[-0.5, 0.5]])
　　I also think that mixing arrays and matrices gives rise to many "happy" debugging hours. However, scipy.sparse matrices are always matrices in terms of 

matrix是array的分支，matrix和array在很多時候都是通用的，你用哪一個都一樣。但這時候，官方建議大家如果兩個可以通用，那就選擇array，因為array更靈活，速度更快，很多人把二維的array也翻譯成矩陣。
但是matrix的優勢就是相對簡單的運算符號，比如兩個矩陣相乘，就是用符號*，但是array相乘不能這么用，得用方法.dot()
array的優勢就是不僅僅表示二維，還能表示3、4、5...維，而且在大部分Python程序里，array也是更常用的。