Run the SageMath code below or simply click here.
load("https://raw.githubusercontent.com/jephianlin/LA-notebook/main/lingeo.py")
### code
set_random_seed(None)
n = 3
A = matrix(n, random_int_list(### code
set_random_seed(None)
n = 3
A = matrix(n, random_int_list(n**2, 2))
for k in range(n + 1):
print("k =", k)
if k == 0:
print("s0 = 1")
else:
sk = 0
print("alpha det(A[alpha])")
for alpha in Combinations(list(range(n)), k):
detAalpha = A[alpha,alpha].determinant()
sk += detAalpha
print(alpha, detAalpha)
print("s%s ="%k, sk)
print("characteristic polynomial:", (-1)**n * A.charpoly())n**2, 2))
print("A =")
print(A)
print()
for k in range(n + 1):
print("k =", k)
if k == 0:
print("s0 = 1")
print()
else:
sk = 0
print("alpha det(A[alpha])")
for alpha in Combinations(list(range(n)), k):
detAalpha = A[alpha,alpha].determinant()
sk += detAalpha
print(alpha, detAalpha)
print("s%s ="%k, sk)
print()
print("characteristic polynomial:", (-1)**n * A.charpoly())
Replace None
with your favorite number and run the code again. The outcome is a matrix
This note can be found at Course website > Learning resources.
or
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