Quasi matrices, orthogonal polynomials, and Lanczos
$\def\sopmatrix#1{ \begin{pmatrix}#1\end{pmatrix} } \def\map[#1]{\mapengine #1,\void.} \def\mapenginesep_#1#2,#3.{\mapfunction{#2}\ifx\void#3\else#1\mapengine #3.\fi } \def\mapsep_#1[#2]{\mapenginesep_{#1}#2,\void.} \def\vcbr[#1]{\pr(#1)} \def\qqand{\qquad\hbox{and}\qquad} \def\qqfor{\qquad\hbox{for}\qquad} \def\qqas{\qquad\hbox{as}\qquad} \def\half{ {1 \over 2} } \def\D{ {\rm d} } \def\I{ {\rm i} } \def\E{ {\rm e} } \def\C{ {\mathbb C} } \def\R{ {\mathbb R} } \def\H{ {\mathbb H} } \def\Z{ {\mathbb Z} } \def\T{ {\cal T} } \def\CC{ {\cal C} } \def\FF{ {\cal F} } \def\HH{ {\cal H} } \def\LL{ {\cal L} } \def\vc#1{ {\mathbf #1} } \def\bbC{ {\mathbb C} } \def\norm#1{\left\| #1 \right\|} \def\pr(#1){\left({#1}\right)} \def\br[#1]{\left[{#1}\right]} \def\acos{{\rm acos}\,} \def\ip#1{ \left\langle{#1}\right\rangle } \def\addtab#1={#1\;&=} \def\ccr{\\\addtab}$ Orthogonal polynomi...