A=(1:3)' * ones(1,3) /// \sleftarrow{\normalfont transpose \verb+'+ and usual matrix product \verb+*+ } A.* A' /// \sleftarrow{\normalfont multiplication tables: using a term-by-term product} t=(1:3)';m=size(t,'r');n=3; A=(t*ones(1,n+1)).^(ones(m,1)*[0:n]) /// \sleftarrow {\begin{minipage}[t]{6cm}{\nf{}term-by-term exponentiation to build\\ a Vandermonde matrix $$A(i,j)= t\sb{i}\sp{j-1}$$ }\end{minipage}} A=eye(2,2).*.[1,2;3,4] /// \sleftarrow{\normalfont Kronecker product} A=[1,2;3,4];b=[5;6]; /// x = A \verb+\+ b ; norm(A*x -b)/// \sleftarrow{\begin{minipage}[t]{6cm}{\nf{}\verb+\+ {for} solving a linear system \verb+Ax=b+.\index{norm@\texttt{norm}} }\end{minipage}} A=[1,2;3,4];b=[5;6]; x = A \b ; norm(A*x -b) /// @@prerequisite ///A1=[A,zeros(A)]; x = A1 \verb+\+ b /// \sleftarrow {\begin{minipage}[t]{6cm}{\nf{}underdetermined system: a solution with \\ minimum norm is returned}\end{minipage}} A1=[A,zeros(A)]; x = A1\b /// /// @@prerequisite ///A1=[A;A]; x = A1\verb+\+ [b;7;8] /// \sleftarrow {\begin{minipage}[t]{6cm}{\nf{}overdetermined system: a least squared \\ solution is returned}\end{minipage}} A1=[A;A]; x = A1\ [b;7;8] /// @@prerequisite