
\newcommand{\tras}{^{\mbox{\tiny T}}}
\newcommand{\mtras}{^{\mbox{\tiny -T}}}
\newcommand{\dtras}{^{\mbox{\tiny T}\dag}}
\newcommand{\muno}{^{\mbox{\tiny -1}}}
\newcommand{\tracon}{^{*}}
\newcommand{\mtracon}{^{-*}}
\newcommand{\ds}{\displaystyle}
\newcommand{\ts}{\textstyle}
\newcommand{\scr}{\scriptstyle}
\newcommand{\sscr}{\scriptscriptstyle}
\newcommand{\bbar}[1]{\bar{\bar{#1}}}

 \newcommand{\evidenzia}[1]{\psframebox[framesep=5pt]{#1}}
 \newcommand{\BoxedEPSF}{\epsfbox} %% Primo capitolo
 \newcommand{\bo}{\mbox{\bf o}}
 \newcommand{\und}{\underline}
 \newcommand{\Span}{\mbox{\rm span}}
 \newcommand{\spann}{\mbox{\rm span}}
 \newcommand{\Agg}{\mbox{\rm agg}}
 \newcommand{\adj}{\mbox{\rm adj}}
 \newcommand{\Imm}{\mbox{\rm Im}}
 \newcommand{\Ker}{\mbox{\rm ker}}
 \newcommand{\rango}{\mbox{\rm rango}}
 \newcommand{\bM}{{\bf M}}
 \newcommand{\mat}[2]{\left[\begin{array}{#1} #2 \end{array}\right]}
 \newcommand{\mdet}[2]{\left|\begin{array}{#1} #2 \end{array}\right|}
 \newcommand{\cofbin}[2]{\left(\!\begin{array}{c}#1\\ #2 \end{array}\!\right)}

% Bold face:
\def\a{{\bf a}} \def\b{{\bf b}} \def\c{{\bf c}} \def\d{{\bf d}}
\def\e{{\bf e}} \def\f{{\bf f}} \def\g{{\bf g}} \def\h{{\bf h}}
\def\ib{{\bf i}} \def\j{{\bf j}} \def\k{{\bf k}} \def\l{{\bf l}}
\def\m{{\bf m}} \def\n{{\bf n}} \def\o{{\bf o}} \def\p{{\bf p}}
\def\q{{\bf q}} \def\r{{\bf r}} \def\s{{\bf s}} \def\t{{\bf t}}
\def\u{{\bf u}} \def\v{{\bf v}} \def\w{{\bf w}} \def\x{{\bf x}}
\def\y{{\bf y}} \def\z{{\bf z}}

\def\A{{\bf A}} \def\B{{\bf B}} \def\C{{\bf C}} \def\D{{\bf D}}
\def\E{{\bf E}} \def\F{{\bf F}} \def\G{{\bf G}} \def\H{{\bf H}}
\def\I{{\bf I}} \def\J{{\bf J}} \def\K{{\bf K}} \def\L{{\bf L}}
\def\M{{\bf M}} \def\N{{\bf N}} \def\O{{\bf O}} \def\P{{\bf P}}
\def\Q{{\bf Q}} \def\R{{\bf R}} \def\S{{\bf S}} \def\T{{\bf T}}
\def\U{{\bf U}} \def\V{{\bf V}} \def\W{{\bf W}} \def\X{{\bf X}}
\def\Y{{\bf Y}} \def\Z{{\bf Z}}

% Calligraphics:

\def\cA{{\cal A}} \def\cB{{\cal B}} \def\cC{{\cal C}} \def\cD{{\cal D}}
\def\cE{{\cal E}} \def\cF{{\cal F}} \def\cG{{\cal G}} \def\cH{{\cal H}}
\def\cI{{\cal I}} \def\cJ{{\cal J}} \def\cK{{\cal K}} \def\cL{{\cal L}}
\def\cM{{\cal M}} \def\cN{{\cal N}} \def\cO{{\cal O}} \def\cP{{\cal P}}
\def\cQ{{\cal Q}} \def\cR{{\cal R}} \def\cS{{\cal S}} \def\cT{{\cal T}}
\def\cU{{\cal U}} \def\cV{{\cal V}} \def\cW{{\cal W}} \def\cX{{\cal X}}
\def\cY{{\cal Y}} \def\cZ{{\cal Z}}

% tilde bold face:

\def\ta{\tilde{\a}} \def\tb{\tilde{\b}} \def\tc{\tilde{\c}}
\def\td{\tilde{\d}} \def\te{\tilde{\e}} \def\tf{\tilde{\f}}
\def\tg{\tilde{\g}} \def\th{\tilde{\h}} \def\tib{\tilde{\i}}
\def\tj{\tilde{\j}} \def\tk{\tilde{\k}} \def\tl{\tilde{\l}}
\def\tm{\tilde{\m}} \def\tn{\tilde{\n}} \def\to{\tilde{\o}}
\def\tp{\tilde{\p}} \def\tq{\tilde{\q}} \def\tr{\tilde{\r}}
\def\tts{\tilde{\s}} \def\ttt{\tilde{\t}} \def\tu{\tilde{\u}}
\def\tv{\tilde{\v}} \def\tw{\tilde{\w}} \def\tx{\tilde{\x}}
\def\ty{\tilde{\y}} \def\tz{\tilde{\z}}

\def\tA{\tilde{\A}} \def\tB{\tilde{\B}} \def\tC{\tilde{\C}}
\def\tD{\tilde{\D}} \def\tE{\tilde{\E}} \def\tF{\tilde{\F}}
\def\tG{\tilde{\G}} \def\tH{\tilde{\H}} \def\tI{\tilde{\I}}
\def\tJ{\tilde{\J}} \def\tK{\tilde{\K}} \def\tL{\tilde{\L}}
\def\tM{\tilde{\M}} \def\tN{\tilde{\N}} \def\tO{\tilde{\O}}
\def\tP{\tilde{\P}} \def\tQ{\tilde{\Q}} \def\tR{\tilde{\R}}
\def\tS{\tilde{\S}} \def\tT{\tilde{\T}} \def\tU{\tilde{\U}}
\def\tV{\tilde{\V}} \def\tW{\tilde{\W}} \def\tX{\tilde{\X}}
\def\tY{\tilde{\Y}} \def\tZ{\tilde{\Z}}

% Overline bold face:

\def\ooa{\overline{\a}} \def\oob{\overline{\b}}
\def\ooc{\overline{\c}} \def\ood{\overline{\d}}
\def\ooe{\overline{\e}} \def\oof{\overline{\f}}
\def\oog{\overline{\g}} \def\ooh{\overline{\h}}
\def\ooib{\overline{\ib}} \def\ooj{\overline{\j}}
\def\ook{\overline{\k}} \def\ool{\overline{\l}}
\def\oom{\overline{\m}} \def\oon{\overline{\n}}
\def\ooo{\overline{\o}} \def\oop{\overline{\p}}
\def\ooq{\overline{\q}} \def\oor{\overline{\r}}
\def\oos{\overline{\s}} \def\oot{\overline{\t}}
\def\oou{\overline{\u}} \def\oov{\overline{\v}}
\def\oow{\overline{\w}} \def\oox{\overline{\x}}
\def\ooy{\overline{\y}} \def\ooz{\overline{\z}}

\def\ooA{\overline{\A}} \def\ooB{\overline{\B}}
\def\ooC{\overline{\C}} \def\ooD{\overline{\D}}
\def\ooE{\overline{\E}} \def\ooF{\overline{\F}}
\def\ooG{\overline{\G}} \def\ooH{\overline{\H}}
\def\ooI{\overline{\I}} \def\ooJ{\overline{\J}}
\def\ooK{\overline{\K}} \def\ooL{\overline{\L}}
\def\ooM{\overline{\M}} \def\ooN{\overline{\N}}
\def\ooO{\overline{\O}} \def\ooP{\overline{\P}}
\def\ooQ{\overline{\Q}} \def\ooR{\overline{\R}}
\def\ooS{\overline{\S}} \def\ooT{\overline{\T}}
\def\ooU{\overline{\U}} \def\ooV{\overline{\V}}
\def\ooW{\overline{\W}} \def\ooX{\overline{\X}}
\def\ooY{\overline{\Y}} \def\ooZ{\overline{\Z}}

% vettoriali:

\def\va{\vec{\a}} \def\vb{\vec{\b}} \def\vc{\vec{\c}}
\def\vd{\vec{\d}} \def\ve{\vec{\e}} \def\vf{\vec{\f}}
\def\vg{\vec{\g}} \def\vh{\vec{\h}} \def\vib{\vec{\i}}
\def\vj{\vec{\j}} \def\vk{\vec{\k}} \def\vl{\vec{\l}}
\def\vm{\vec{\m}} \def\vn{\vec{\n}} \def\vo{\vec{\o}}
\def\vp{\vec{\p}} \def\vq{\vec{\q}} \def\vr{\vec{\r}}
\def\vts{\vec{\s}} \def\vtt{\vec{\t}} \def\vu{\vec{\u}}
\def\vv{\vec{\v}} \def\vw{\vec{\w}} \def\vx{\vec{\x}}
\def\vy{\vec{\y}} \def\vz{\vec{\z}}

\def\vA{\vec{\A}} \def\vB{\vec{\B}} \def\vC{\vec{\C}}
\def\vD{\vec{\D}} \def\vE{\vec{\E}} \def\vF{\vec{\F}}
\def\vG{\vec{\G}} \def\vH{\vec{\H}} \def\vI{\vec{\I}}
\def\vJ{\vec{\J}} \def\vK{\vec{\K}} \def\vL{\vec{\L}}
\def\vM{\vec{\M}} \def\vN{\vec{\N}} \def\vO{\vec{\O}}
\def\vP{\vec{\P}} \def\vQ{\vec{\Q}} \def\vR{\vec{\R}}
\def\vS{\vec{\S}} \def\vT{\vec{\T}} \def\vU{\vec{\U}}
\def\vV{\vec{\V}} \def\vW{\vec{\W}} \def\vX{\vec{\X}}
\def\vY{\vec{\Y}} \def\vZ{\vec{\Z}}

% cappello:

\def\ha{\hat{\a}} \def\hb{\hat{\b}} \def\hc{\hat{\c}}
\def\hd{\hat{\d}} \def\he{\hat{\e}} \def\hf{\hat{\f}}
\def\hg{\hat{\g}} \def\hh{\hat{\h}} \def\hib{\hat{\i}}
\def\hj{\hat{\j}} \def\hk{\hat{\k}} \def\hl{\hat{\l}}
\def\hm{\hat{\m}} \def\hn{\hat{\n}} \def\ho{\hat{\o}}
\def\hp{\hat{\p}} \def\hq{\hat{\q}} \def\hr{\hat{\r}}
\def\hts{\hat{\s}} \def\htt{\hat{\t}} \def\hu{\hat{\u}}
\def\hv{\hat{\v}} \def\hw{\hat{\w}} \def\hx{\hat{\x}}
\def\hy{\hat{\y}} \def\hz{\hat{\z}}

\def\hA{\hat{\A}} \def\hB{\hat{\B}} \def\hC{\hat{\C}}
\def\hD{\hat{\D}} \def\hE{\hat{\E}} \def\hF{\hat{\F}}
\def\hG{\hat{\G}} \def\hH{\hat{\H}} \def\hI{\hat{\I}}
\def\hJ{\hat{\J}} \def\hK{\hat{\K}} \def\hL{\hat{\L}}
\def\hM{\hat{\M}} \def\hN{\hat{\N}} \def\hO{\hat{\O}}
\def\hP{\hat{\P}} \def\hQ{\hat{\Q}} \def\hR{\hat{\R}}
\def\hS{\hat{\S}} \def\hT{\hat{\T}} \def\hU{\hat{\U}}
\def\hV{\hat{\V}} \def\hW{\hat{\W}} \def\hX{\hat{\X}}
\def\hY{\hat{\Y}} \def\hZ{\hat{\Z}}
