Manuals/calci/FROBENIUS
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MATRIX("FROBENIUS",order)
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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 |