• 紅色 基座標(豎著看)
  1 0
  0 1

• 綠色 變換矩陣(豎著看)
  3 1
  0 2

• 藍色 特徵向量(豎著看)
  1−2√2
  02√2

• 黑色 變換矩陣（左乘）特徵向量(豎著看)
  3−2√
  02√

特徵向量與特徵值得幾何含義：
特徵向量：原始向量在進行線性旋轉變換（左乘矩陣）後仍留在其所張成的空間的向量。
特徵值：即特徵向量進行線性變換後，留在原空間中變換的比例。

# -*- coding: utf-8 -*-
"""
Created on Wed Mar 11 18:51:08 2015
@author: Duncan
A simplified version of linearring.py, one of the shapely examples
"""
 


from matplotlib import pyplot as plt
from shapely.geometry.polygon import Polygon
from descartes import PolygonPatch
import numpy as np

def drawArrow1(B,c="data",):

    # fc: filling color
    # ec: edge color
    if c=='data':
        fc='r'
        ec='r'
        s=0.25
    elif c=='transf':
        fc='g'
 

        ec='g'
        s=0.15
    elif c=='eigenv':
        fc='b'
        ec='b'
        s=0.1
    else:
        fc='k'
        ec='k'
        s=0.08

    ax.arrow(0, 0, B[0], B[1],
             length_includes_head=True,# 增加的長度包含箭頭部分
             head_width=s, head_length=s, fc=fc, ec=ec,label='abc')
    # 注意： 預設顯示範圍[0,1][0,1],需要單獨設定圖形範圍，以便顯示箭頭
 

    ax.set_xticks(np.linspace(-3,4,8))
    ax.set_yticks(np.linspace(-1,4,6))
    ax.set_aspect('equal') #x軸y軸等比例

#%%
fig, ax = plt.subplots()
data_origin = np.array([[1,0],[0,1]]) 
data_transf = np.array([[3,1],[0,2]]).T
data = np.vstack((data_origin,data_transf))
c = ['data','data','transf','transf']
for i,j in zip(data,c):
    drawArrow1(i,j)
#%%
D,V = np.linalg.eig(data_transf.T)
c = ['eigenv','eigenv']
for i,j in zip(V.T,c):
    print(i,j)
    drawArrow1(i,j)
ax.grid()
#%%
dt = np.dot(data_transf.T,V).T
drawArrow1(dt[0],c='after transfer')
drawArrow1(dt[1],c='after transfer')
print(dt)
#%%
ring_mixed = Polygon([(0, 0), V.T[0], V.T[1]])
ring_patch = PolygonPatch(ring_mixed,fc='yellow', ec='yellow', alpha=0.5)
ax.add_patch(ring_patch)
#%%
plt.savefig('arrow.png', transparent = True, bbox_inches = 'tight', pad_inches = 0.25)