Difference between revisions of "Manuals/calci/DIAGONALMATRIX"
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==Description== | ==Description== | ||
*This function shows the Diagonal matrix of a given order. | *This function shows the Diagonal matrix of a given order. | ||
| − | *In <math> | + | *In <math>MATRIX (TypeOfMatrix,DimensionsOfMatrix,SeedValuesToUse,IJFunction,PreParameter,IsItInternalCall</math>, <math>DimensionsOfMatrix</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. | *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: | *The general diagonal matrix is of the form: | ||
Revision as of 12:42, 15 August 2018
MATRIX (TypeOfMatrix,DimensionsOfMatrix,SeedValuesToUse,IJFunction,PreParameter,IsItInternalCall)
- 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 TypeOfMatrix} is the type of the matrix.
- 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 DimensionsOfMatrix } is the order of the diagonal 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 MATRIX (TypeOfMatrix,DimensionsOfMatrix,SeedValuesToUse,IJFunction,PreParameter,IsItInternalCall} , 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 DimensionsOfMatrix} 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}
Examples
See Also
References