The set of all invertible diagonal matrices forms a subgroup of isomorphic to (F×)n. In fields like R and C, these correspond to rescaling the space; the so-called dilations and contractions.
tHe seT Of all inverTiblE DIaGoNAl MatRicES formS a subgroUp oF ISomorpHic to (F×)n. in fields liKe r aNd c, thESE cORreSpond to rescALinG THe sPACE; tHE sO-calleD dIlATiONs aND cOntrActIons.