For a
matrix

**, if there is vector***A***and value***x**λ*, such that it holds:
then

**is called its eigenvector and***x**λ*is called its eigenvalue.
It is said
that vector

**is in the same direction as***x***(which is exceptional property). The parameter***Ax**λ*expresses whether and how much the vector shrinks or stretches.
It follows
that multiplying the eigenvector by power of λ

^{p}is like multiplying it*p*times by the matrix**:***A*
There may
exist multiple eigenvectors and eigenvalues. All vectors

**can be found by solving equation:***x*
This
equation has a non-zero solution only if the determinant of the matrix is zero.
In according, the parameters

*λ*can be found by solving equation:**For example**the two eigenvectors and eigenvalues for the

*2x2*matrix:

Additional
properties of

*nxn*matrix**are the***A***trace**(sum of diagonal elements) which is sum of eigenvalues:
and the

**determinant**which is product of eigenvalues:
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