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The eigenvectors of a square matrix

`A`

are all

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non-zero vectors

`v`

such that

`Av=\lambda v`

for some scalar

`\lambda `

, called the eigenvalue For example if

`A=([5,1,-1],[4,2,-4],[3,-3,1])`

then we can directly calculate that

`([5,1,-1],[4,2,-4],[3,-3,1])([1],[0],[1])=`

`◻`

9.

`([5,1,-1],[4,2,-4],[3,-3,1])([1],[0],[1])=`

a So we have demonstrated that

`([1],[0],[1])`

is an eigenvector with eigenvalue Number Note: the Maple notation for the vector

`([1],[2],[3])`

is

`{`

(

`:<1,2,3:)`

} Similarly we can check that

`([0],[1],[1])`

is an eigenvector with eigenvalue

`([1],[1],[0])`

is an eigenvector with eigenvalue

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