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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- Jul 24th 2012, 05:32 PMcomputersLinear Algebra
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) - Jul 24th 2012, 05:47 PMpickslidesRe: Linear Algebra
The bounds will be for each row $\displaystyle a_{ii} \pm \sum |a_{ij}|$ where $\displaystyle i \neq j$

- Jul 24th 2012, 06:21 PMcomputersRe: Linear Algebra
can u please explain further as to how to do the problem

- Jul 24th 2012, 06:56 PMpickslidesRe: Linear Algebra
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? - Jul 24th 2012, 07:11 PMcomputersRe: Linear Algebra
for second = 5 +- 3/2

for third = 6 +- 1

for fourth = -3+- 7/4

for fifth = 4 +- 1 - Jul 24th 2012, 07:25 PMcomputersRe: Linear Algebra
what are the real and imaginary eigen values of the matrix

- Jul 24th 2012, 07:29 PMpickslidesRe: Linear Algebra
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.