If I tell you to take a toy cube and say “you can turn this around and stretch it however you want” then you will have some axes about which you can turn it and some directions in which you will strech it. The arrows pointing in the direction of streching or the axes about which you turn are the eigenvectors. If you turn it about multiple axes, and strech it in multiple directions, there are some simple rules about how you have to add those up.
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