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linalg::invhilbert -- inverse of a Hilbert matrix

Introduction

linalg::invhilbert(n) returns the inverse of the n x n Hilbert matrix H. The n x n Hilbert matrix H is defined by H[i,j]:= 1/(i+j-1).

Call(s)

linalg::invhilbert(n <, R>)

Parameters

n - the dimension of the matrix: a positive integer
R - the component ring: a domain of category Cat::Rng; default: Dom::ExpressionField()

Returns

an n x n matrix of the domain Dom::Matrix(R).

Related Functions

linalg::hilbert

Details

Example 1

We compute the inverse of the 3 x 3 Hilbert matrix:

>> A := linalg::invhilbert(3)
                           +-                 -+
                           |   9,   -36,  30   |
                           |                   |
                           |  -36,  192, -180  |
                           |                   |
                           |   30, -180,  180  |
                           +-                 -+

This is a matrix of the domain Dom::Matrix().

If you prefer a different component ring, the matrix may be converted into the desired domain afterwards (see convert, for example). Alternatively, one can specify the component ring when calling linalg::invhilbert, for example the domain Dom::Float:

>> A := linalg::invhilbert(3, Dom::Float)
                        +-                       -+
                        |   9.0,   -36.0,  30.0   |
                        |                         |
                        |  -36.0,  192.0, -180.0  |
                        |                         |
                        |   30.0, -180.0,  180.0  |
                        +-                       -+
>> domtype( A )
                          Dom::Matrix(Dom::Float)

Background

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