>>> import numpy as np

>>> a=np.array([[1,2,3],[4,5,6],[7,8,9]])
>>> a
array([[1, 2, 3],
    [4, 5, 6],
    [7, 8, 9]])
>>> b=a.copy()
>>> b
array([[1, 2, 3],
    [4, 5, 6],
    [7, 8, 9]])
>>> a+b#多維數(shù)組的加減,按對(duì)應(yīng)位置操作
array([[ 2, 4, 6],
    [ 8, 10, 12],
    [14, 16, 18]])
>>> a*3#多維數(shù)組乘常數(shù),則對(duì)數(shù)組中每一個(gè)元素乘該常數(shù)
array([[ 3, 6, 9],
    [12, 15, 18],
    [21, 24, 27]])
>>> np.dot(a,b)#數(shù)組的點(diǎn)乘運(yùn)算通過np.dot(a,b)來實(shí)現(xiàn),相當(dāng)于矩陣乘
array([[ 30, 36, 42],
    [ 66, 81, 96],
    [102, 126, 150]])
>>> c=np.array([1,2,3])#構(gòu)造一行三列的數(shù)組
>>> c
array([1, 2, 3])
>>> c*a#c為一行三列,放于數(shù)組a之前,則對(duì)數(shù)組a中每行對(duì)應(yīng)位置相乘
array([[ 1, 4, 9],
    [ 4, 10, 18],
    [ 7, 16, 27]])
>>> a*c#c為一行三列,放于數(shù)組a之后,依舊是對(duì)數(shù)組a中每行對(duì)應(yīng)位置相乘
array([[ 1, 4, 9],
    [ 4, 10, 18],
    [ 7, 16, 27]])
>>> #如果想要矩陣運(yùn)算,則需要np.dot()函數(shù)
>>> np.dot(c,a)#c為一行三列,放于數(shù)組a之前,按正常矩陣方式運(yùn)算
array([30, 36, 42])
>>> np.dot(a,c)#c為一行三列,放于數(shù)組a之后,相當(dāng)于矩陣a乘以3行一列的c矩陣,返回結(jié)果值不變,格式為1行3列
array([14, 32, 50])
>>> #將c改為多行一列的形式
>>> d=c.reshape(3,1)
>>> d
array([[1],
    [2],
    [3]])
>>> #
>>> np.dot(a,d)#值與np.dot(a,c)一致,但格式以改變?yōu)?行1列
array([[14],
    [32],
    [50]])
 
>>> a*a#數(shù)組使用*的運(yùn)算其結(jié)果屬于數(shù)組運(yùn)算,對(duì)應(yīng)位置元素之間的運(yùn)算
array([[ 1, 4, 9],
    [16, 25, 36],
    [49, 64, 81]])
>>> #但是不能更改a,d點(diǎn)乘的位置,不符合矩陣運(yùn)算格式
>>> np.dot(d,a)
Traceback (most recent call last):
 File "<pyshell#28>", line 1, in <module>
  np.dot(d,a)
ValueError: shapes (3,1) and (3,3) not aligned: 1 (dim 1) != 3 (dim 0)

>>> a=np.array([[1,2,3],[4,5,6],[7,8,9]])
>>> a=np.mat(a)
>>> a
matrix([[1, 2, 3],
    [4, 5, 6],
    [7, 8, 9]])
>>> b=a
>>> b
matrix([[1, 2, 3],
    [4, 5, 6],
    [7, 8, 9]])
>>> a+b#矩陣的加減運(yùn)算和數(shù)組運(yùn)算一致
matrix([[ 2, 4, 6],
    [ 8, 10, 12],
    [14, 16, 18]])
>>> a-b
matrix([[0, 0, 0],
    [0, 0, 0],
    [0, 0, 0]])
>>> a*b#矩陣的乘用*即可表示
matrix([[ 30, 36, 42],
    [ 66, 81, 96],
    [102, 126, 150]])
>>> np.dot(a,b)#與*一致
matrix([[ 30, 36, 42],
    [ 66, 81, 96],
    [102, 126, 150]])
>>> b*a
matrix([[ 30, 36, 42],
    [ 66, 81, 96],
    [102, 126, 150]])
>>> np.dot(b,a)
matrix([[ 30, 36, 42],
    [ 66, 81, 96],
    [102, 126, 150]])
>>> c=np.array([1,2,3])#構(gòu)造一行三列數(shù)組
>>> c
array([1, 2, 3])
>>> c*a#矩陣運(yùn)算
matrix([[30, 36, 42]])
>>> a*c#不合矩陣規(guī)則
Traceback (most recent call last):
 File "<pyshell#63>", line 1, in <module>
  a*c
 File "F:\python3\anzhuang\lib\site-packages\numpy\matrixlib\defmatrix.py", line 309, in __mul__
  return N.dot(self, asmatrix(other))
ValueError: shapes (3,3) and (1,3) not aligned: 3 (dim 1) != 1 (dim 0)
>>> np.dot(c,a)#和矩陣運(yùn)算一致
matrix([[30, 36, 42]])
>>> np.dot(a,c)#自動(dòng)將a轉(zhuǎn)換成3行1列參與運(yùn)算,返回結(jié)果格式已經(jīng)變?yōu)?行3列而非3行一列的矩陣
matrix([[14, 32, 50]])
>>> c=c.reshape(3,1)
>>> c
array([[1],
    [2],
    [3]])
>>> a*c#和矩陣運(yùn)算一致
matrix([[14],
    [32],
    [50]])
>>> c*a#不合矩陣運(yùn)算格式
Traceback (most recent call last):
 File "<pyshell#71>", line 1, in <module>
  c*a 
ValueError: shapes (3,1) and (3,3) not aligned: 1 (dim 1) != 3 (dim 0)

>>> a
matrix([[1, 2, 3],
    [4, 5, 6],
    [7, 8, 9]])
>>> a.T
matrix([[1, 4, 7],
    [2, 5, 8],
    [3, 6, 9]])
>>> a.H#共軛轉(zhuǎn)置
matrix([[1, 4, 7],
    [2, 5, 8],
    [3, 6, 9]])
>>> b=np.eye(3)*3
>>> b
array([[3., 0., 0.],
    [0., 3., 0.],
    [0., 0., 3.]])
>>> b=np.mat(b)
>>> b.I#求逆運(yùn)算
matrix([[0.33333333, 0.    , 0.    ],
    [0.    , 0.33333333, 0.    ],
    [0.    , 0.    , 0.33333333]])
>>> np.trace(b)#求跡運(yùn)算
9.0