Physical significance of eigen vectors of Covariance matrix

[dexterdev]

Hi all,

I have a doubt regarding the physical significance of eigen vectors of the covariance matrix. I came to know that eigen vectors of covariance matrix are the principal components for dimensionality reduction etc, but how to prove it?

 

[D H]

That's the definition of principal components. How can you prove a definition?

 

[dexterdev]

OK Sir, I was not knowing that it was a definition. Let me ask one thing...How researchers arrive at definitions. ie here when ever you find eigen vectors of covariance matrix (which is symmetrical matrix) you find them orthogonal and regression scatter plot lies of the significant PCA1 and least significant PCA2 has less strength points (noise etc). Is definitions formed from observation. Just to know these sort of things since I have no access to any professors.