The Distance command computes the distance (the norm of the difference) between two matrices or two vectors with respect to a specified p-norm. For more information on various norms that can be computed, see Student,LinearAlgebra,Norm.

If A and B are both matrices then p must be one of 1, 2, infinity, Frobenius, or Euclidean.

If A and B are both vectors then p must be one of a non-negative number, infinity, -infinity, Frobenius, or Euclidean.

A and B must both be either vectors or matrices, not one of each.

$\mathrm{with}\left(\mathrm{Student}\left[\mathrm{NumericalAnalysis}\right]\right)\:$

$A≔\mathrm{Matrix}\left(\left[\left[1.432\,5.223\,6.444\right]\,\left[5.325\,7.453\,8.223\right]\,\left[6.432\,8.343\,8.222\right]\right]\right)$

$A≔\left[\begin{array}{ccc}1.432& 5.223& 6.444\\ 5.325& 7.453& 8.223\\ 6.432& 8.343& 8.222\end{array}\right]$

$B≔\mathrm{Matrix}\left(\left[\left[5.224\,9.809\,8.932\right]\,\left[0.424\,8.453\,3.532\right]\,\left[2.533\,9.435\,0.423\right]\right]\right)$

$B≔\left[\begin{array}{ccc}5.224& 9.809& 8.932\\ 0.424& 8.453& 3.532\\ 2.533& 9.435& 0.423\end{array}\right]$

$\mathrm{Distance}\left(A\,B\,\mathrm{\infty }\right)$

$12.790$

$\mathrm{Distance}\left(A\,B\,\mathrm{Frobenius}\right)$

$12.87808806$

$\mathrm{Distance}\left(A\,B\,1\right)$

$14.978$

$a≔\mathrm{Vector}\left(\left[\left[2.42\,5.34\right]\,\left[8.78\,0.42\right]\right]\right)$

$a≔\left[\begin{array}{c}2.42\\ 5.34\\ 8.78\\ 0.42\end{array}\right]$

$b≔\mathrm{Vector}\left(\left[\left[4.32\,9.32\right]\,\left[6.22\,1.33\right]\right]\right)$

$b≔\left[\begin{array}{c}4.32\\ 9.32\\ 6.22\\ 1.33\end{array}\right]$

$\mathrm{Distance}\left(a\,b\,3.1\right)$

$4.401239994$

$\mathrm{Distance}\left(a\,b\,-\mathrm{\infty }\right)$

$0.91$