# Manuals/calci/EIGENVALUES

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**EIGENVALUES (Matrix)**

- is the array of numeric elements.

## Description

- This function shows the Eigen value of the given matrix.
- In , is any matrix values.
- In linear algebra, an eigen vector or characteristic vector of a linear transformation is a non-zero vector whose direction does not change when that linear transformation is applied to it.
- Let A be a linear transformation represented by a matrix A.
- Let A is an nxn matrix, v is a non zero nx1 vector and is a scalar which may be either real or complex.
- Any value of for which this equation has a solution is known as an eigenvalue of the matrix A.
- It is sometimes also called the characteristic value.
- The vector, v, which corresponds to this value is called an eigenvector.
- The eigenvalue problem can be rewritten as .
- If v is non-zero, this equation will only have a solution if .
- This equation is called the characteristic equation of A, and is an nth order polynomial in with n roots.
- These roots are called the eigenvalues of A.

## Examples

A | B | C | |
---|---|---|---|

1 | 3 | 7 | 5 |

2 | 10 | 12 | 8 |

3 | 6 | 8 | 14 |

=EIGENVALUES(A1:C3)

-2.018987498930866 |
25.303239119591886 |
5.715748379338994 |

-0.8195524172935329 0.3557792393359474 0.2128903683040517 |
0.5726193656991498 0.663334322125492 0.6212592923173481 |
0.02099755544415341 0.6583378387635402 -0.7541316747045657 |

A | B | |
---|---|---|

1 | 5 | 6 |

2 | 9 | -11 |

=EIGENVALUES(A1:B2)

-13.862780491200214 |
7.8627804912002155 |

0.3031213645114406 0.9025310769284506 |
-0.9529519601620652 0.43062472662211493 |