# Documentation

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# `linalg`::`vandermonde`

Vandermonde matrix

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## Syntax

```linalg::vandermonde(`[v1, v2, …]`, <`R`>)
```

## Description

```linalg::vandermonde(v1, v2, ... , vn)``` returns the n×n Vandermonde matrix V with entries Vij = vij - 1.

Use ```linalg::vandermonde([v1, ..., vn], R)``` to define the n×n Vandermonde matrix over the field `R`. Note that the Vandermonde nodes vi must be elements of `R` or must be convertible to elements of `R`.

Vandermonde matrices of dimension n×n can be inverted with O(n2) operations. Linear equations with a Vandermonde coefficient matrix can be solved via `linalg::vandermondeSolve`.

## Examples

### Example 1

Create a 3×3 Vandermonde matrix:

`V := linalg::vandermonde([v1, v2, v3])`

`V` is a matrx of the domain `Dom::Matrix()`.

`domtype(V)`

You can specify a special component ring for the matrices, provided the nodes can be converted to elements of the ring. For example, specification of the domain `Dom::Float` generates floating-point entries:

`V := linalg::vandermonde([2, PI, 1/3], Dom::Float)`

`domtype(V)`

`delete V`

## Parameters

 `v1, v2, …` The Vandermonde nodes: arithmetical expressions `R` The component ring: a domain of category `Cat::Rng`; default: `Dom::ExpressionField``()`

## Return Values

n×n matrix of the domain `Dom::Matrix``(R)`.

## Algorithms

Vandermonde matrices are notoriously ill-conditioned. The inverses of large floating-point Vandermonde matrices are subject to severe round-off effects.