m = Table[ 1/(i+j+1),{i,1,3},{j,1,3}]

Inverse[m]

% . m

Det[ m - x IdentityMatrix[3] ]

NSolve[ % == 0 , x]

Eigenvalues[ N[m] ]

Eigenvalues[ Table[Random[], {100},{100}] ];

ListPlot[ Transpose[ {Re[%], Im[%]} ]]

MatrixForm[ {{0,a},{a,b}} ]

Simplify[ Eigenvectors[%] ]

Eigenvalues[ %% ]

1+ x^2 + 3 x^3 /. x -> 1 + a

f[n_] := n^2

f[3] + 1 / f [a+b]

fac[n_] := n fac[n-1]

fac[1] := 1

?fac

fac[30]

Gamma[31]

mylog[x_ y_] := mylog[x] + mylog[y]

mylog[ a b c ]

g/: g[x_] + g[y_] := g[x + y]

g[a] + g[b] + g[c]