Manuals/calci/FROBENIUS

MATRIX("FROBENIUS",order)

• $order$ 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:

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

1. MATRIX("frobenius")

1	0	0
0	1	0
0	0.7699975343421102	1

See Also

• ANTIDIAGONAL
• CONFERENCE
• CIRCULANT
• HANKEL