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")