Difference between revisions of "Manuals/calci/FROBENIUS"

Revision as of 13:03, 23 April 2015

MATRIX("FROBENIUS",order)

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:

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.

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-<div style="font-size:30px">'''FROBENIUS'''</div><br/>
+<div style="font-size:30px">'''MATRIX("FROBENIUS",order)'''</div><br/>
+*<math>order</math> 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:
+#1.All entries on the main diagonal are ones
+#2.The entries below the main diagonal of at most one column are arbitrary
+#3.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==