האקספוננט של מטריצה

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

function addScaled(A, B, scale) {
  return A.map((row, i) => row.map((value, j) => value+scale*B[i][j]));
}

function expSeries(A, t, terms=28) {
  let sum = [[1, 0], [0, 1]];
  let term = [[1, 0], [0, 1]];
  for (let k=1; k<terms; k++) {
    term = matMul(term, A);
    term = term.map(row => row.map(value => value*t/k));
    sum = addScaled(sum, term, 1);
  }
  return sum;
}

const J = [[1, 1], [0, 1]];
const t = 0.5;
const exact = Math.exp(t);
console.log("series", expSeries(J, t));
console.log("exact", [[exact, t*exact], [0, exact]]);
console.log("at zero", expSeries(J, 0));

from math import exp

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 add_scaled(A, B, scale):
    return [[value+scale*B[i][j] for j, value in enumerate(row)]
            for i, row in enumerate(A)]

def exp_series(A, t, terms=28):
    total = [[1, 0], [0, 1]]
    term = [[1, 0], [0, 1]]
    for k in range(1, terms):
        term = mat_mul(term, A)
        term = [[value*t/k for value in row] for row in term]
        total = add_scaled(total, term, 1)
    return total

J = [[1, 1], [0, 1]]
t = 0.5
exact = exp(t)
print("series", exp_series(J, t))
print("exact", [[exact, t*exact], [0, exact]])
print("at zero", exp_series(J, 0))