# Manuals/calci/FROBENIUS

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**MATRIX("FROBENIUS",order)**

- is the order of the matrix.

## Description

- This function gives the matrix with the property of Frobenius.
- A Frobenius matrix is a special kind of square matrix from numerical mathematics.
- A square matrix is a Frobenius matrix if it has the following three properties:

- All entries on the main diagonal are ones
- The entries below the main diagonal of at most one column are arbitrary
- Every other entry is zero.

- And also Frobenius matrices are invertible.
- The inverse of a Frobenius matrix is again a Frobenius matrix, equal to the original matrix with changed signs outside the main diagonal.
- Here MATRIX("frobenius") gives the frobenius matrix of order 3.
- In calci, users can get a different order of matrices also.

## Examples

- MATRIX("frobenius") = 1
- MATRIX("frobenius",3)

1 | 0 | 0 |

0 | 1 | 0 |

0 | 0.7699975343421102 | 1 |