Difference between revisions of "Manuals/calci/FROBENIUS"
Jump to navigation
Jump to search
| (2 intermediate revisions by 2 users not shown) | |||
| Line 15: | Line 15: | ||
==Examples== | ==Examples== | ||
| − | #MATRIX("frobenius") | + | #MATRIX("frobenius") = 1 |
| + | #MATRIX("frobenius",3) | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
| Line 24: | Line 25: | ||
| 0 || 0.7699975343421102 || 1 | | 0 || 0.7699975343421102 || 1 | ||
|} | |} | ||
| + | |||
| + | ==Related Videos== | ||
| + | |||
| + | {{#ev:youtube|i0JGx8PEQW8|280|center|Norm of Matrix}} | ||
==See Also== | ==See Also== | ||
| Line 32: | Line 37: | ||
==References== | ==References== | ||
| + | *[http://en.wikipedia.org/wiki/Frobenius_matrix Frobenius matrix] | ||
Latest revision as of 00:53, 26 October 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
- MATRIX("frobenius",3)
| 1 | 0 | 0 |
| 0 | 1 | 0 |
| 0 | 0.7699975343421102 | 1 |