# Linear Algebra

• Jul 24th 2012, 06:32 PM
computers
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)
• Jul 24th 2012, 06:47 PM
pickslides
Re: Linear Algebra
The bounds will be for each row $a_{ii} \pm \sum |a_{ij}|$ where $i \neq j$
• Jul 24th 2012, 07:21 PM
computers
Re: Linear Algebra
can u please explain further as to how to do the problem
• Jul 24th 2012, 07:56 PM
pickslides
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?
• Jul 24th 2012, 08:11 PM
computers
Re: Linear Algebra
for second = 5 +- 3/2
for third = 6 +- 1
for fourth = -3+- 7/4
for fifth = 4 +- 1
• Jul 24th 2012, 08:25 PM
computers
Re: Linear Algebra
what are the real and imaginary eigen values of the matrix
• Jul 24th 2012, 08:29 PM
pickslides
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.