hilb — Hilbert Matrix


\begin{rail} Hilbert : 'hilb' '(' Scalar ')' ; \end{rail}
hilb generates a Hilbert matrix. The scalar argument specifies the dimensions of the square matrix to be generated. This is also known as the order of the Hilbert matrix. If we have a Hilbert matrix of order n, and row and column indicies of i and j respectively, then the matrix elements are given by

aij = $\displaystyle {\frac{{1}}{{i+j-1}}}$

$\Longrightarrow$ This is not an built-in function. This function is normally loaded on start-up from the hilb.r file in the standard rlib directory. Use of the -r option, incorrectly setting the RLAB_LIB_DIR environmental variable, or modifying hilb.r may make this function unavailable.
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