>
> restart;
> with( linalg );
Warning, the protected names norm and trace have been redefined and unprotected
>
> A := hilbert( 5 );
![A := matrix([[1, 1/2, 1/3, 1/4, 1/5], [1/2, 1/3, 1/...](images/linalg9.gif)
> B := map( evalf, A );
>
> st := time():
> inverse( A );
> time()-st;
![matrix([[25, -300, 1050, -1400, 630], [-300, 4800, ...](images/linalg11.gif)
>
> st := time():
> inverse( B );
> time()-st;
>
> st := time():
> LUdecomp( A, P='p', L='l', U='u' ):
> print( p, l, u );
> time()-st;
![matrix([[1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 1,...](images/linalg15.gif)
>
> st := time():
> C := eigenvectors( B );
> time()-st;
> Lambda := diag( op( map2( op, 1, [C] ) ) );
![Lambda := matrix([[.2085342184, 0, 0, 0, 0], [0, .3...](images/linalg23.gif)
> U := transpose( matrix( map2( op, [3,1], [C] ) ) );
>
> evalm( A &* U - U &* Lambda );
>
>
> restart;
> with( linalg );
Warning, the protected names norm and trace have been redefined and unprotected
>
> A := hilbert( 25 );
> B := map( evalf, A );
>
> st := time():
> inverse( A );
> time()-st;
>
> st := time():
> inverse( B );
> time()-st;
>
> st := time():
> LUdecomp( A, P='p', L='l', U='u' ):
> print( p, l, u );
> time()-st;
>
> st := time():
> C := eigenvectors( B );
> time()-st;
> Lambda := diag( op( map2( op, 1, [C] ) ) );
> U := transpose( matrix( map2( op, [3,1], [C] ) ) );
>
> evalm( A &* U - U &* Lambda );
>