1、转置对于二维数组有用,对一位数组无效
2、理解特征值和特征向量的对应关系
a=np.array([[1 ,2, 3],[4, 5, 6],[7, 8, 9]]) a Out[27]: array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) w,v = LA.eig(a) w Out[29]: array([ 1.61168440e+01, -1.11684397e+00, -1.30367773e-15]) v Out[30]: array([[-0.23197069, -0.78583024, 0.40824829], [-0.52532209, -0.08675134, -0.81649658], [-0.8186735 , 0.61232756, 0.40824829]]) a Out[31]: array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) #dot(a[:,:], v[:,i]) = w[i] * v[:,i] w[0] Out[33]: 16.116843969807043 v[:,0] Out[34]: array([-0.23197069, -0.52532209, -0.8186735 ]) w[0]*v[:,0] Out[35]: array([ -3.73863537, -8.46653421, -13.19443305]) np.dot(a[:,:],v[:,0]) Out[37]: array([ -3.73863537, -8.46653421, -13.19443305]) a Out[38]: array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) v[:,0] Out[39]: array([-0.23197069, -0.52532209, -0.8186735 ]) 1*-0.23197069+2*-0.52532209+3*-0.8186735 Out[40]: -3.73863537 4*-0.23197069+5*-0.52532209+6*-0.8186735 Out[41]: -8.46653421 v[:,0] Out[42]: array([-0.23197069, -0.52532209, -0.8186735 ]) v[:,0].T Out[43]: array([-0.23197069, -0.52532209, -0.8186735 ]) w[0] Out[44]: 16.116843969807043 w[0]*v[:,0] Out[45]: array([ -3.73863537, -8.46653421, -13.19443305]) a Out[46]: array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) a.T Out[47]: array([[1, 4, 7], [2, 5, 8], [3, 6, 9]]) c = v[0] c Out[49]: array([-0.23197069, -0.78583024, 0.40824829]) c.T Out[50]: array([-0.23197069, -0.78583024, 0.40824829])
a Out[55]: array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) a*v[:,0] Out[56]: array([[-0.23197069, -1.05064419, -2.4560205 ], [-0.92788275, -2.62661047, -4.912041 ], [-1.62379481, -4.20257675, -7.36806149]]) v[:,0] Out[57]: array([-0.23197069, -0.52532209, -0.8186735 ])
y = a*v[:,0] y Out[59]: array([[-0.23197069, -1.05064419, -2.4560205 ], [-0.92788275, -2.62661047, -4.912041 ], [-1.62379481, -4.20257675, -7.36806149]]) np.sum(y[0,:]) Out[63]: -3.7386353719172973 np.sum(y[1,:]) Out[64]: -8.4665342116284013 np.sum(y[2,:]) Out[65]: -13.194433051339505
时间: 2024-10-29 10:45:58