Manuals/calci/DIAGONALMATRIX

DIAGONALMATRIX(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 or order of the matrix.

Description

• This function shows the Diagonal matrix of a given order.
• In 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 DIAGONALMATRIX(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 order of square matrix.
• A diagonal matrix is a square matrix which is of the form 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_{ij}=c_{i} \delta_{ij}} where 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 \delta_{ij}} is the Kronecker delta, 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 c_{i}} are constants, and i,j=1, 2, ..., n.
• The general diagonal matrix is of the form:

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 \begin{bmatrix} c_{1} & 0 & \cdots & 0 \\ 0 & c_{2} & \cdots & 0 \\ \vdots & \vdots &\ddots & \vdots \\ 0 & 0 & \cdots & c_{n} \end{bmatrix} }

• So the main diagonal entries are need not to be zero and off-diagonal entries are zero.
• That is,the matrix D = (di,j) with n columns and n rows is diagonal if:

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 \forall i,j \isin {1,2,....n},i \ne j \rArr d_{i,j} = 0}

See Also

• DIAGONALFILL
• ARROWHEAD
• MATRIXOPERATORS

References

• Diagonal matrix

• List of Main Z Functions

• Z3 home