Difference between revisions of "Manuals/calci/FROBENIUS"
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*A Frobenius matrix is a special kind of square matrix from numerical mathematics. | *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: | *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. | *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. | *The inverse of a Frobenius matrix is again a Frobenius matrix, equal to the original matrix with changed signs outside the main diagonal. | ||
| Line 15: | Line 15: | ||
==Examples== | ==Examples== | ||
| + | #MATRIX("frobenius") | ||
| + | {| class="wikitable" | ||
| + | |- | ||
| + | | 1 || 0 || 0 | ||
| + | |- | ||
| + | | 0 || 1 || 0 | ||
| + | |- | ||
| + | | 0 || 0.7699975343421102 || 1 | ||
| + | |} | ||
| + | |||
| + | ==See Also== | ||
| + | *[[Manuals/calci/ANTIDIAGONAL| ANTIDIAGONAL]] | ||
| + | *[[Manuals/calci/CONFERENCE| CONFERENCE]] | ||
| + | *[[Manuals/calci/CIRCULANT| CIRCULANT]] | ||
| + | *[[Manuals/calci/HANKEL| HANKEL]] | ||
| + | |||
| + | ==References== | ||
Revision as of 14:21, 23 April 2015
MATRIX("FROBENIUS",order)
- is the order of the matrix.
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 | 0 | 0 |
| 0 | 1 | 0 |
| 0 | 0.7699975343421102 | 1 |