notes / updates | linear algebra

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January 23, 2026 | Visualizing Discrete Dynamic Systems with SageMath

   
A = matrix(RR,[[0.8,0],[0,1.1]]) # matrix A
x = vector([1.0,2.0])  #initial population

mylist = []  #create an empty list
mylist.append(x) #add the initial population vector

iterations = 25; #set the number of iterations
for i in range(1,iterations):   
    x = A*x
    mylist.append(x)

#just to check the content of mylist
for j in range(0,iterations):
       print(mylist[j][0],mylist[j][1])

# or simply print the whole thing
mylist

#build plot
myplot = arrow(mylist[0],mylist[1])

for i in range(1,iterations):
    myplot += arrow(mylist[i-1],mylist[i])

myplot.show()

# after the list has been filled, we reset
x = vector([1.0,2.0])