# Math Help - Linear Algebra

1. ## Linear 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)

2. ## Re: Linear Algebra

The bounds will be for each row $a_{ii} \pm \sum |a_{ij}|$ where $i \neq j$

3. ## Re: Linear Algebra

can u please explain further as to how to do the problem

4. ## Re: Linear Algebra

For the first row $\displaystyle 3\pm (|0|+|-1|+|-0.25|+|0.25|) = 3\pm\frac{3}{2}$

What do you get for the second?

5. ## Re: Linear Algebra

for second = 5 +- 3/2
for third = 6 +- 1
for fourth = -3+- 7/4
for fifth = 4 +- 1

6. ## Re: Linear Algebra

what are the real and imaginary eigen values of the matrix

7. ## Re: 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.