My Math Forum Question on eigenvector calculation

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October 30th, 2016, 07:47 PM   #1
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Question on eigenvector calculation

I have a question regarding one example of eigenvector calculation.

In Equation (1) of the attached example, should the first column of matrix A be written as 0.8x1 + 0.2x2 , rather than x1 + 0.2x2 ?

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 October 30th, 2016, 08:45 PM #2 Senior Member     Joined: Sep 2015 From: USA Posts: 2,375 Thanks: 1276 no. $x_1 = (0.6, 0.4)$ $x_2 = (1,-1)$ $(0.8,0.2) = 1 \cdot(0.6,0.4) + 0.2 \cdot (1,-1)$
 October 31st, 2016, 05:41 AM #3 Newbie   Joined: Oct 2016 From: Singapore Posts: 11 Thanks: 0 Hi romsek, thanks for the response. Could you explain where the factors of 1 and 0.2 came from? Thanks
October 31st, 2016, 10:07 AM   #4
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Quote:
 Originally Posted by mikeraj Hi romsek, thanks for the response. Could you explain where the factors of 1 and 0.2 came from? Thanks
it's a matter of projecting the vector $(0.8,0.2)$ onto the two non-orthogonal unit eigenvectors.

Answer 0 at projective geometry - Equation for non-orthogonal projection of a point onto two vectors representing the isometric axis? - Mathematics Stack Exchange

details one way of going about that.

 October 31st, 2016, 09:07 PM #5 Newbie   Joined: Oct 2016 From: Singapore Posts: 11 Thanks: 0 Many thanks, romsek!

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