According to Wikipedia ("Diagonal Matrix", 8-Dec-2019,
https://en.wikipedia.org/wiki/Diagonal_matrix): "In linear algebra,
a *diagonal matrix* is a matrix in which the entries outside the main diagonal
are all zero; the term usually refers to square matrices." The diagonal
matrices are mentioned in [Lang] p. 576, but without giving them a dedicated
definition. Furthermore, "A diagonal matrix with all its main diagonal entries
equal is a *scalar matrix*, that is, a scalar multiple of the
identity matrix . Its effect on a vector is scalar multiplication by
[see scmatscm!]". The scalar multiples of the identity matrix are
mentioned in [Lang] p. 504, but without giving them a special name.

The main results of this subsection are the definitions of the sets of diagonal and scalar matrices (df-dmat and df-scmat), basic properties of (elements of) these sets, and theorems showing that the diagonal matrices are a subring of the ring of square matrices (dmatsrng), that the scalar matrices are a subring of the ring of square matrices (scmatsrng), that the scalar matrices are a subring of the ring of diagonal matrices (scmatsrng1) and that the ring of scalar matrices (over a commutative ring) is a commutative ring (scmatcrng).

- cdmat
- cscmat
- df-dmat
- df-scmat
- dmatval
- dmatel
- dmatmat
- dmatid
- dmatelnd
- dmatmul
- dmatsubcl
- dmatsgrp
- dmatmulcl
- dmatsrng
- dmatcrng
- dmatscmcl
- scmatval
- scmatel
- scmatscmid
- scmatscmide
- scmatscmiddistr
- scmatmat
- scmate
- scmatmats
- scmateALT
- scmatscm
- scmatid
- scmatdmat
- scmataddcl
- scmatsubcl
- scmatmulcl
- scmatsgrp
- scmatsrng
- scmatcrng
- scmatsgrp1
- scmatsrng1
- smatvscl
- scmatlss
- scmatstrbas
- scmatrhmval
- scmatrhmcl
- scmatf
- scmatfo
- scmatf1
- scmatf1o
- scmatghm
- scmatmhm
- scmatrhm
- scmatrngiso
- scmatric
- mat0scmat
- mat1scmat