```
Eigenvectors(matrix)
```

get the numerical eigenvectors of the

`matrix`

.

See

- Wikipedia - Eigenvalues and Eigenvectors
- Youtube - Eigenvectors and eigenvalues | Essence of linear algebra, chapter 14

```
>> Eigenvectors({{1,0,0},{0,1,0},{0,0,1}})
{{1.0,0.0,0.0},{0.0,1.0,0.0},{0.0,0.0,1.0}}
```

**Note:** Symjas implementation of the `Eigenvectors`

function adds zero vectors when the geometric multiplicity of the eigenvalue is smaller than its algebraic multiplicity (hence the regular eigenvector matrix should be non-square).
With these additional null vectors, the `Eigenvectors`

result matrix becomes square.
This happens for example with the following square matrix:

```
>> Eigenvectors({{1,0,0},{-2,1,0},{0,0,1}})
{{-2.50055*10^-13,1.0,0.0},{0.0,0.0,1.0},{0.0,0.0,0.0}}
>> Eigenvalues({{1,0,0},{-2,1,0},{0,0,1}})
{1.0,1.0,1.0}
```

Its characteristic polynomial is `(1.0-\[lambda])^3.0`

, hence is has one eigen value `\[lambda]==1.0`

with algebraic multiplicity `3`

. However, this eigenvalue leads to only two eigenvectors
`v1 = {0.0, 1.0, 0.0}`

and `v2 = {0.0, 0.0, 1.0}`

, hence its geometric multiplicity is only `2`

, not `3`

.
So we add a third zero vector `v3 = {0.0, 0.0, 0.0}`

.

Eigensystem, Eigenvalues, CharacteristicPolynomial

- ☑ - partially implemented

Feedback

Tell us anything that can be improved