= Hilbert matrix
{c}
{title2=$H_{ij}=\frac1{i+j-1},\quad1\leq i,j\leq n$}
{wiki}
A real <symmetric matrix> whose entries are the moments $H_{ij}=\int_0^1x^{i-1}x^{j-1}dx$. Thus it is the <Gram matrix> of the monomials in the real <L2 inner product> on $[0,1]$. For a nonzero real coefficient vector $v$, $v^THv=\int_0^1(\sum_i v_ix^{i-1})^2dx>0$, so every finite Hilbert matrix is <positive-definite>. The moment description connects these matrices with polynomial approximation and with the <shifted Hilbert quadratic-form bound>.
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