Important: The linalg package has been deprecated. Use the superseding command LinearAlgebra[DotProduct], instead.

- For information on migrating linalg code to the new packages, see examples/LinearAlgebraMigration.

If called with only two arguments, dotprod computes the vector dot product using the standard definition for a vector space over the complex field: sum u[i]*conjugate(v[i]), as i ranges over the length of u and v.

If the third argument 'orthogonal' is specified, dotprod will compute the vector dot product using the definition: sum u[i]*v[i], as i ranges over the length of u and v.

If u and v are real vectors, then the two forms of dotprod are equivalent.

The command with(linalg,dotprod) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{linalg}\right)\:$

$u≔\mathrm{vector}\left(\left[1\,x\,y\right]\right)$

$u≔\left[\begin{array}{ccc}1& x& y\end{array}\right]$

$v≔\mathrm{vector}\left(\left[1\,0\,0\right]\right)$

$v≔\left[\begin{array}{ccc}1& 0& 0\end{array}\right]$

$\mathrm{dotprod}\left(u\,v\right)$

$1$

$a≔\left[1\,\mathrm{I}\right]\;$$b≔\left[\mathrm{I}\,1\right]$

$a≔\left[1\,\mathrm{I}\right]$

$b≔\left[\mathrm{I}\,1\right]$

$\mathrm{dotprod}\left(a\,b\right)$

$0$

$\mathrm{dotprod}\left(a\,b\,'\mathrm{orthogonal}'\right)$

$2\mathrm{I}$