Singular spectrum analysis and their "eigentriplets"

Question

I am struggling to understand why eigentriplets arise when decomposing a signal by using singular spectrum analysis (SSA).

The term eigentriples refers to the components of a singular value decomposition (U, S, V).

When the reconstructed component are almost identical, it is said that they are "eigentriplets", because they have almost the same eigentripels.

To this extent I ought to clarify what is happening and why I still have this confusion, so here is an example code and the output of theirof:

import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
Number of elements in a series
N = 1000
Series abscissa
n = np.linspace(0, 360*10, N)
"""
s0 is linear vector with values going linearly from 0 to 3.6
s1 is a periodic sinusoid with magnitude 2
s2 is a dampened sinusoid with values starting at 2 and decreasing
s  is all of the above mentioned signal plus random noise
""" 
s0 = n/1000
s1 = 2np.sin(10n)
s2 = 2np.exp(-n/N)np.sin(50*n)

s = s0 + s1 + s2 + np.random.normal(0,1,N)
plt.figure()
plt.plot(n, s)
plt.xlabel("n")
plt.ylabel("Time Series")
plt.title("Example for Stack Exchange")

Then this signal will be taken through the SSA algorithm with an optimal window length of N/2. So it goes through this code:

# Getting window length L and lagged length K
L = 500-1
K = N - L + 1
Constructing the time lagged Hankel matrix
X=np.zeros((K,L))
for m in range (0, L):
    X[:,m] = s[m:K+m]
Trajectory matrix
Cemb = np.dot(X.T,X)/K
Eigen decomposition
eigenValues, eigenVectors = np.linalg.eig(Cemb)
idx = eigenValues.argsort()[::-1]

eigenValues = eigenValues[idx]
eigenVectors = eigenVectors[:,idx]
Vectors of Principal Components
PC = np.dot(X,eigenVectors)
Pre-allocating Reconstructed Component Matrix
RC = np.zeros((N, L))
Reconstruct the elementary matrices without storing them
for i in range(L):
    myBuf = np.outer(PC[:,i], eigenVectors[:,i].T)
    myBuf = myBuf[::-1]
    RC[:,i] = [myBuf.diagonal(j).mean()

               for j in range(-myBuf.shape[0]+1, myBuf.shape[1])]
First 6 RC
fig, ax = plt.subplots(3,2)
ax = ax.flatten()
for i in range (0, 6):
    ax[i].plot(RC[:,i])
    ax[i].set_title(str(i))
plt.tight_layout()

We get these results, where we start to see that component 1 and 2 are the same, as well as 3 and 4. I can also see that the magnitude of s1 and s2 are also divided there. This is what I am not getting: why is this happening exactly ?

Here is also the pairwise weighted correlation of these vectors:

For references, please see:

https://www.mathworks.com/matlabcentral/mlc-downloads/downloads/submissions/58967/versions/2/previews/html/SSA_beginners_guide_v7.html

https://en.wikipedia.org/wiki/Singular_spectrum_analysis

Any help is appreciated, thank you so much for reading! :D