Manuals/calci/VANDERMONDE

MATRIX("VANDERMONDE",order)

• $order$ 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:

$V={\begin{bmatrix}1&\alpha _{1}&\alpha _{1}^{2}&\dots &\alpha _{1}^{n-1}\\1&\alpha _{2}&\alpha _{2}^{2}&\dots &\alpha _{2}^{n-1}\\1&\alpha _{3}&\alpha _{3}^{2}&\dots &\alpha _{3}^{n-1}\\\vdots &\vdots &\vdots &\ddots &\vdots \\1&\alpha _{m}&\alpha _{m}^{2}&\dots &\alpha _{m}^{n-1}\end{bmatrix}}$

• 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

Related Videos

Vandermonde Determinant

See Also

• SYMMETRIC
• PASCAL
• TRIANGULAR

References

• Vandermonde Matrix