Manuals/calci/VANDERMONDE

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	0.9070418316405267	0.8227248843458015
1	0.9100837279111147	0.8282523918085919
1	0.9911492799874395	0.9823768952196198

• 2.MATRIX("vandermonde",4,10..14)

1	10	100	1000
1	11	121	1331
1	12	144	1728
1	13	169	2197

Related Videos

Vandermonde Determinant

See Also

• SYMMETRIC
• PASCAL
• TRIANGULAR

References

• Vandermonde Matrix