Eigenvectors and Eigenvalues

[Jeffrey Chudy]

Eigenvectors and Eigenvalues

[Anonymous]

Q94 – If you were to plot two vectors (2,0,1,3) and (-1,2,2,0) what angle would be between them.

The answer says to calculate the dot product of the vectors and divide by the product of the length of the vectors. Since the dot product = 0, then you know the vectors are perpendicular and the angle is 90 degrees.

If I try to plot these vectors, I get an angle of about 45 degrees. I’m plotting (2,0) (1,3) and (-1,2) (2,0). The (2,0) appears twice, so this is where the two lines intersect. Where does the 90 degrees come from?

In the tutorial on Eignenvalues, the example is plotted (-1,2)(2,1) with both points drawn (0,0) creating a 90 degree angle. This one is obvious, but how do you get 90 degrees from Question 94 above?

Thanks!

[Anonymous]

(2,0,1,3) is a single point on a 4 dimensional plane – not the same thing as 2,0 and 1,3. You cannot plot a 4 dimensional thing graphically, certainly not on a 2 dimensional plane. The example in the tutorial is completely different, it just illustrates the concept with a simple 2 dimensional vector.

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