From:

\(A=\begin{bmatrix}

1 & 0 & 0\\

0 & 0 & 1\\

0 & 1 & 2\\

2 & 2 & 1\\

1 & 0 & 0\\

2 & 3 & 2\\

\end{bmatrix}

\)

I first had to calculate the gravity point g (1,1,1), Y the centered data matrix

\(Y=\begin{bmatrix}

-1 & -1 & -1\\

-1 & -1 & 0\\

-1 & 0 & 1\\

1 & 1 & 0\\

0 & -1 & -1\\

1 & 2 & 1\\

\end{bmatrix}\)

and V the covariance matrix with \(V=\frac{1}{n}Y^tY\)

\(

V=\begin{bmatrix}

4 & 4 & 0\\

4 & 8 & 4\\

0 & 4 & 4\\

\end{bmatrix}\)

There is three eigen vectors but only two eigen vectors non associated with a null eigen value:

\(v_1=\begin{bmatrix}

1\\

0\\

-1

\end{bmatrix}v_2=\begin{bmatrix}

1\\

2\\

1

\end{bmatrix}\)

After normalizing the vectors, projecting Y (the matrix above centralized and normed) on the plane described by the two eigen-vectors, I get the following principal componant analysis:

\(C=\{\frac{C_1}{\sqrt{\lambda_1}},\frac{C_2}{\sqrt{\lambda_2}}\}\)

\(C=\frac{\sqrt{3}}{2}

\begin{bmatrix}

1 & -1\\

-1 & -1\\

-1 & 0\\

1 & 1\\

1 & -1\\

0 & 2\\

\end{bmatrix}\)

I then had to display graphically the cloud N'I) of all elements on the factorial plan defined by the two first factorial axes. Furthermore, I have to coment this graphical displaying.

My teacher asked

And I have no idea...

And then

\(A=\begin{bmatrix}

1 & 0 & 0\\

0 & 0 & 1\\

0 & 1 & 2\\

2 & 2 & 1\\

1 & 0 & 0\\

2 & 3 & 2\\

\end{bmatrix}

\)

I first had to calculate the gravity point g (1,1,1), Y the centered data matrix

\(Y=\begin{bmatrix}

-1 & -1 & -1\\

-1 & -1 & 0\\

-1 & 0 & 1\\

1 & 1 & 0\\

0 & -1 & -1\\

1 & 2 & 1\\

\end{bmatrix}\)

and V the covariance matrix with \(V=\frac{1}{n}Y^tY\)

\(

V=\begin{bmatrix}

4 & 4 & 0\\

4 & 8 & 4\\

0 & 4 & 4\\

\end{bmatrix}\)

There is three eigen vectors but only two eigen vectors non associated with a null eigen value:

\(v_1=\begin{bmatrix}

1\\

0\\

-1

\end{bmatrix}v_2=\begin{bmatrix}

1\\

2\\

1

\end{bmatrix}\)

After normalizing the vectors, projecting Y (the matrix above centralized and normed) on the plane described by the two eigen-vectors, I get the following principal componant analysis:

\(C=\{\frac{C_1}{\sqrt{\lambda_1}},\frac{C_2}{\sqrt{\lambda_2}}\}\)

\(C=\frac{\sqrt{3}}{2}

\begin{bmatrix}

1 & -1\\

-1 & -1\\

-1 & 0\\

1 & 1\\

1 & -1\\

0 & 2\\

\end{bmatrix}\)

I then had to display graphically the cloud N'I) of all elements on the factorial plan defined by the two first factorial axes. Furthermore, I have to coment this graphical displaying.

My teacher asked

**what can I tell from there?**And I have no idea...

And then

**How can I say which individual contributes the most to inertia of the first factorial axe (the eigen vector non associated with a null value)?**

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