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October 30th, 2016, 08:47 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 ?

Thanks in advance for your inputs.
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October 30th, 2016, 09:45 PM   #2
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no.

$x_1 = (0.6, 0.4)$
$x_2 = (1,-1)$

$(0.8,0.2) = 1 \cdot(0.6,0.4) + 0.2 \cdot (1,-1)$
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October 31st, 2016, 06:41 AM   #3
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Hi romsek, thanks for the response.

Could you explain where the factors of 1 and 0.2 came from?

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October 31st, 2016, 11:07 AM   #4
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Quote:
Originally Posted by mikeraj View Post
Hi romsek, thanks for the response.

Could you explain where the factors of 1 and 0.2 came from?

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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.
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October 31st, 2016, 10:07 PM   #5
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Many thanks, romsek!
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