ערכים עצמיים ווקטורים עצמיים

function eigenvalues2x2(A) {
  const trace = A[0][0] + A[1][1];
  const determinant = A[0][0] * A[1][1] - A[0][1] * A[1][0];
  const discriminant = trace ** 2 - 4 * determinant;
  if (discriminant < 0) {
    const real = trace / 2;
    const imaginary = Math.sqrt(-discriminant) / 2;
    return [{ real, imaginary }, { real, imaginary: -imaginary }];
  }
  const root = Math.sqrt(discriminant);
  return [(trace - root) / 2, (trace + root) / 2];
}

function anchorSolution(t) {
  const slow = Math.exp(2 * t);
  const fast = Math.exp(6 * t);
  return [slow + fast, -slow + 3 * fast];
}

const A = [[3, 1], [3, 5]];
console.log("eigenvalues =", eigenvalues2x2(A));
for (const t of [0, 0.25, 0.5]) {
  console.log({ t, y: anchorSolution(t) });
}

from math import exp, sqrt

def eigenvalues_2x2(A):
    trace = A[0][0] + A[1][1]
    determinant = A[0][0]*A[1][1] - A[0][1]*A[1][0]
    discriminant = trace**2 - 4*determinant
    if discriminant < 0:
        real = trace/2
        imaginary = sqrt(-discriminant)/2
        return [(real, imaginary), (real, -imaginary)]
    root = sqrt(discriminant)
    return [(trace-root)/2, (trace+root)/2]

def anchor_solution(t):
    slow, fast = exp(2*t), exp(6*t)
    return [slow+fast, -slow+3*fast]

A = [[3, 1], [3, 5]]
print("eigenvalues =", eigenvalues_2x2(A))
for t in [0, 0.25, 0.5]:
    print(t, anchor_solution(t))