Manuals/calci/TRIDIAGONAL

MATRIX("TRIDIAGONAL",order)

• $order$ is the size of the Tridiagonal matrix.

Description

• This function returns the matrix with the property of tridiagonal.
• A square matrix with nonzero elements only on the diagonal and slots horizontally or vertically adjacent the diagonal.
• i.e., along the subdiagonal and superdiagonal.
• So a tridiagonal matrix is a matrix that has nonzero elements only on the main diagonal, the first diagonal below this, and the first diagonal above the main diagonal.
• A tridiagonal is of the form:

${\begin{vmatrix}a_{11}&a_{12}&0&0&\cdots &\cdots &0&0\\a_{21}&a_{22}&a_{23}&\cdots &\cdots &\cdots &0&0\\0&a_{32}&a_{33}&\cdots &\cdots &\ddots &a_{n-2,n-1}&0\\\vdots &\vdots &\ddots &\ddots &\ddots &\ddots &a_{n-1,n-1}&a_{n-1,n}\\0&0&\cdots &\cdots &\cdots &\cdots &a_{n,n-1}&a_{nn}\\\end{vmatrix}}$

• A general tridiagonal matrix is not necessarily symmetric or Hermitian,but tridiagonal matrix is a matrix that is both upper and lower Hessenberg matrix.
• In Calci, MATRIX("tridiagonal") gives the tridiagonal matirx of order 3.
• Users can change the order of the matrix.

Examples

• MATRIX("tridiagonal")

59	58	0
-93	3	21
0	-24	90

• MATRIX("tridiagonal",6)

23	9	0	0	0	0
-6	91	-75	0	0	0
0	32	-25	-11	0	0
0	0	-44	42	-1	0
0	0	0	61	-26	86
0	0	0	0	-50	-92

See Also

• ANTIDIAGONAL
• BIDIAGONAL
• PENTADIAGONAL
• TRIANGULAR

References

• Tridiagonal Matrix