apply gershgorin's theorem to the problem of bounding the real and imaginary parts of the eigen values of the matrix A = (3, 0, -1, -1/4, 1/4) (0, 5, 1/2, 0, 1) (-1/4, 0, 6, 1/4, 1/2) (0, -1, 1/2, -3, 1/4) (1/6, -1/6, 1/3, 1/3, 4)
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The bounds will be for each row $\displaystyle a_{ii} \pm \sum |a_{ij}|$ where $\displaystyle i \neq j$
can u please explain further as to how to do the problem
For the first row $\displaystyle \displaystyle 3\pm (|0|+|-1|+|-0.25|+|0.25|) = 3\pm\frac{3}{2}$ What do you get for the second?
for second = 5 +- 3/2 for third = 6 +- 1 for fourth = -3+- 7/4 for fifth = 4 +- 1
what are the real and imaginary eigen values of the matrix
Looks like you have the hang of it. You are required to plot those intervals on the real(x)/imaginary(y) axis. In your case they all sit on x.
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