取至：机器学习算法原理与编程实践（郑捷）
# -*- coding: utf-8 -*-
# Filename : matrix05.py
import operator
from numpy import *
eps = 1.0e-6 # 误差量
# 矩阵的特征值和特征向量
A = mat([[8,1,6],[3,5,7],[4,9,2]])
evals, evecs = linalg.eig(A)
print "特征值:",evals,"
特征向量:", evecs
# 手动计算特征值：
m,n = shape(A)
# Aeig = lambda*I-A = [[lambda-8,-1],[-6;-3,lambda-5,-7],[-4,-9,lambda-2]]
# (lambda-8)*(lambda-5)*(lambda-2)-190-24*(5-lambda)-3*(2-lambda)-63*(8-lambda)
equationA = [1,-15,-24,360] #得到系数方程矩阵
evals = roots(equationA) # 计算矩阵方程的根
print "特征值:" ,evals
# 特征值和特征向量,还原原矩阵
sigma = evals*eye(m)
print evecs*sigma*linalg.inv(evecs)
