Book
Linear Algebra
Author
Gilbert Strang
Edition
def is_uniq(l):
a=set()
for i in l:
a.add(i)
b= list(a)
if len(l)==len(b):
return True
else:
return False
def is_diag(X):
l=X.eigenvalues()
if is_uniq(l):
return True
else:
return False
def diagonalize(X):
if is_diag(X):
a= X.eigenvectors_right()
l=[]
for i in a:
l.append(list(i[1][0]))
S=transpose(matrix(l))
D=(S^(-1))*X*S
return D,S
else:
print "not diag"
A1=matrix([[4,3],[1,2]])
D=diagonalize(A1)[0]
S=diagonalize(A1)[1]
#A1=S*D*S**(-1)
#Therefore A^(k)=S*D^(k)*S**(-1)
S*D^(100)*S**(-1)
out:[5916456789157588540587964239620896722549048263317672535777091979980469 5916456789157588540587964239620896722549048263317672535777091979980468]
[1972152263052529513529321413206965574183016087772557511925697326660156 1972152263052529513529321413206965574183016087772557511925697326660157]
#Therefore this matrix A^100
Solution by:
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