Manuals/calci/BIDIAGONAL

MATRIX("BIDIAGONAL",order)

• Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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")