import numpy as np
import numpy.linalg as alg
import matplotlib.pyplot as plt

A = np.array([[4,1,1],[1,4,1],[1,1,4]])
B = np.array([[10,9,10],[9,8,9],[10,9,10]])

def sym(M) :
    n = M.shape[0]
    for i in range(n) :
        for j in range(n) :
            if M[i,j] != M[j,i] :
                return False
    return True

def def_sym(M) :
    if not sym(M) :
        return False
    L = alg.eigvals(M)
    for x in L :
        if x <= 0 :
            return False
    return True

T = np.linspace(0,1,100)
Y = []
for t in T :
    y = -np.log(alg.det((1-t)*A+t*B))
    Y.append(y)
plt.plot(T,Y)
plt.show()