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.
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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
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