Difference between revisions of "Manuals/calci/DIAGONALMATRIX"
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| − | diagonal | + | <div style="font-size:30px">'''DIAGONALMATRIX(Order)'''</div><br/> |
| + | *<math>Order</math> is the size or order of the matrix. | ||
| + | |||
| + | ==Description== | ||
| + | *This function shows the Diagonal matrix of a given order. | ||
| + | *In <math>DIAGONALMATRIX(Order)</math>, <math>Order</math> is the order of square matrix. | ||
| + | *A diagonal matrix is a square matrix which is of the form <math>a_{ij}=c_{i} \delta_{ij}</math> where <math>delta_{ij}</math> is the Kronecker delta, <math>c_{i}</math> are constants, and i,j=1, 2, ..., n. | ||
| + | *The general diagonal matrix is of the form: | ||
| + | <math>\begin{bmatrix} | ||
| + | c_{1} & 0 & \cdots & 0 \\ | ||
| + | 0 & c_{2} & \cdots & 0 \\ | ||
| + | \vdots & \vdots &\ddots & \vdots \\ | ||
| + | 0 & 0 & \cdots & c_{n} | ||
| + | \end{bmatrix} </math> | ||
| + | As stated above, the off-diagonal entries are zero. That is, the matrix A = (ai,j) with n columns and n rows is diagonal if | ||
Revision as of 12:47, 6 June 2017
DIAGONALMATRIX(Order)
- is the size or order of the matrix.
is the size or order of the matrix.Description
- This function shows the Diagonal matrix of a given order.
- In , is the order of square matrix.
- A diagonal matrix is a square matrix which is of the form where Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\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:
, 
where Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\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.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} } As stated above, the off-diagonal entries are zero. That is, the matrix A = (ai,j) with n columns and n rows is diagonal if