português

Abstract

The distance between two affine subspaces is usually obtained by calculating
the projection of a certain vector onto a certain subspace.
This can be avoided by using the Cramer's rule and the determinant of a certain Gram matrix.
In this letter we show how to combine these two tools to obtain a formula for the distance
between two affine subspaces. The famous formulas for the distance from point to line in
$\mathbb{R}^2$ and for the distance from point to plane in $\mathbb{R}^3$ are instances
of this more general formula.