Difference between revisions of "Manuals/calci/VANDERMONDE"
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==Examples== | ==Examples== | ||
| − | *1.MATRIX("vandermonde") | + | *1.MATRIX("vandermonde") =1 |
| + | *2.MATRIX("vandermonde",3) | ||
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| 1 || 0.9911492799874395 || 0.9823768952196198 | | 1 || 0.9911492799874395 || 0.9823768952196198 | ||
|} | |} | ||
| − | * | + | *3.MATRIX("vandermonde",4,10..14) |
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| 1 || 13 || 169 || 2197 | | 1 || 13 || 169 || 2197 | ||
|} | |} | ||
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| + | ==Related Videos== | ||
| + | |||
| + | {{#ev:youtube|87iJTcXqTKY|280|center|Vandermonde Determinant}} | ||
==See Also== | ==See Also== | ||
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==References== | ==References== | ||
| + | *[http://en.wikipedia.org/wiki/Vandermonde_matrix Vandermonde Matrix] | ||
Latest revision as of 01:46, 26 October 2015
MATRIX("VANDERMONDE",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 Vandermonde matrix.
Description
- This function gives the matrix with the property of vandermonde.
- A Vandermonde matrix is a matrix presents a geometric progression in every row or in every column with the first element being 1.
- A Vandermonde matrix of order n 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 V=\begin{bmatrix} 1 & \alpha_1 & \alpha_1^2 & \dots & \alpha_1^{n-1}\\ 1 & \alpha_2 & \alpha_2^2 & \dots & \alpha_2^{n-1}\\ 1 & \alpha_3 & \alpha_3^2 & \dots & \alpha_3^{n-1}\\ \vdots & \vdots & \vdots & \ddots &\vdots \\ 1 & \alpha_m & \alpha_m^2 & \dots & \alpha_m^{n-1} \end{bmatrix} }
- A Vandermonde matrix is sometimes also called an alternant matrix.
- Users can assign the numbers for vandermonde matrix. For e.g.,MATRIX("vandermonde",10,1..10)
Examples
- 1.MATRIX("vandermonde") =1
- 2.MATRIX("vandermonde",3)
| 1 | 0.9070418316405267 | 0.8227248843458015 |
| 1 | 0.9100837279111147 | 0.8282523918085919 |
| 1 | 0.9911492799874395 | 0.9823768952196198 |
- 3.MATRIX("vandermonde",4,10..14)
| 1 | 10 | 100 | 1000 |
| 1 | 11 | 121 | 1331 |
| 1 | 12 | 144 | 1728 |
| 1 | 13 | 169 | 2197 |