1. ## Eigenvectors

Does anyone know how to:
Show that the matrix B=

[php]
-4 1 0 . . 0 1
1 -4 1 0 . . 0
0 1 -4 1 .. . .
: : : : 0
0 . . 0 1 -4 1
1 0 . . 0 1 -4
[/php]

has v=
[php]
1
1
1
.
:
1
1
[/php]
as an eigenvector.

2. Originally Posted by smiler
Does anyone know how to:
Show that the matrix B=

[php]
-4 1 0 . . 0 1
1 -4 1 0 . . 0
0 1 -4 1 .. . .
: : : : 0
0 . . 0 1 -4 1
1 0 . . 0 1 -4
[/php]

has v=
[php]
1
1
1
.
:
1
1
[/php]
as an eigenvector.
As every row of the matrix has three non-zero elements 1,1,-4 every element of the matrix times your vector is -2, and so your vector is an eigen-vector of the matrix corresponding to e-value -2.

ZB