Manuals/calci/BIDIAGONAL

MATRIX("BIDIAGONAL",order)

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

Description

• This function returns the matrix with the property of bidiagonal.
• A bidiagonal matrix has non zero entries only on the main bidiagonal and either the first super-diagonal and first sub-diagonal.
• In Calci,users will get different types of bidiagonal matrices.
• There are two types are there lower bidiagonal and upper bidiagonal.
• When the diagonal below the main diagonal has the non-zero entries the matrix is lower bidiagonal.
• When the diagonal above the main diagonal has the non-zero entries the matrix is upper bidiagonal.
• The example of lower bidiagonal matrix is:

$A={\begin{pmatrix}62&0&0&0\\-60&69&0&0\\0&-52&65&0\\0&0&-18&1\\\end{pmatrix}}$

• The example of a upper bidiagonal matrix is:

$A={\begin{pmatrix}56&18&0&0\\0&-33&-55&0\\0&0&-2&-60\\0&0&0&-9\\\end{pmatrix}}$

• The syntax of lower and upper bidiagonal matrices are MATRIX("lowerbidiagonal") or MATRIX("lower-bidiagonal") and MATRIX("upperbidiagonal") or MATRIX("upper-bidiagonal")

Examples

• 1.MATRIX("bidiagonal")

-63	97	0
0	44	65
0	0	97

• 2.MATRIX("bidiagonal",5)

77	-7	0	0	0
0	83	56	0	0
0	0	2	-88	0
0	0	0	-88	-59
0	0	0	0	87

• 3.MATRIX("upper-bidiagonal")

-5	40	0
0	5	71
0	0	19

• 4.MATRIX("lowerbidiagonal",4)

87	0	0	0
8	-13	0	0
0	-70	82	0
0	0	94	-33

See Also

• PERSYMMETRIC
• PASCAL
• TRIANGULAR