לכסון, חזקות ומה עלול להיכשל

function matVec(A, v) {
  return A.map(row => row.reduce((sum, value, j) => sum+value*v[j], 0));
}

function matMul(A, B) {
  return A.map(row => B[0].map((_, j) =>
    row.reduce((sum, value, k) => sum+value*B[k][j], 0)));
}

function matrixPower(A, n) {
  let result = [[1, 0], [0, 1]];
  let factor = A.map(row => [...row]);
  for (let k=n; k>0; k=Math.floor(k/2)) {
    if (k%2) result = matMul(result, factor);
    if (k>1) factor = matMul(factor, factor);
  }
  return result;
}

const A = [[3, 1], [3, 5]];
const n = 3;
const modal = [2**n+6**n, -(2**n)+3*6**n];
console.log("modal", modal);
console.log("power", matVec(matrixPower(A, n), [2, 2]));
console.log("defective J^5", matrixPower([[1, 1], [0, 1]], 5));

def mat_vec(A, v):
    return [sum(a*b for a, b in zip(row, v)) for row in A]

def mat_mul(A, B):
    columns = list(zip(*B))
    return [[sum(a*b for a, b in zip(row, column))
             for column in columns] for row in A]

def matrix_power(A, n):
    result = [[1, 0], [0, 1]]
    factor = [row[:] for row in A]
    while n:
        if n % 2:
            result = mat_mul(result, factor)
        n //= 2
        if n:
            factor = mat_mul(factor, factor)
    return result

A = [[3, 1], [3, 5]]
n = 3
modal = [2**n+6**n, -(2**n)+3*6**n]
print("modal", modal)
print("power", mat_vec(matrix_power(A, n), [2, 2]))
print("defective J^5", matrix_power([[1, 1], [0, 1]], 5))