WOLFRAM|DEMONSTRATIONS PROJECT

Eigenvectors by Hand

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matrix

2
1
-1
-1


-1
1
1
1

0
-1
1
0
0
2
1
0

0
-1
1
2

A linear map transforms vectors into other vectors. A nonzero vector (boldface in this Demonstration) is an eigenvector when its image (dotted here) is a multiple of itself; this occurs when the colored parallelogram vanishes. Drag the vectors until they become eigenvectors. If you manage to hit a basis of eigenvectors, then in this new basis the matrix of the linear map (shown above the graphic) becomes diagonal.