[Scilab-users] Empty matrix

[Rafael Guerra]

Hi Christophe,

Quite impressive summary.

Fyi, the following reference on empty matrices algebra is extremelly good (and it even refers to de Boor memo and some previous ideas on the subject):

Nett, C. N.  and W. M. Haddad [1993] "A system-theoretic appropriate realization of the empty matrix concept," IEEE Transactions on Automatic Control, vol. 38, no. 5, pp. 771-775

Nett and Haddad define empty matrices of size []mxn and argue that "the empty matrix concept has the  potential to provide an elegant, general means for transparently  handling special cases in matrix formulas corresponding to the absence of one or more of the matrices involved."

Another interesting message from that article:
" ... we have purposely avoided any and all discussion of anything but the purely algebraic properties of empty matrices. For example, we have purposely not discussed the determinant, eigenvalues, singular values, or norm of an empty matrix. The reason for this is because we feel strongly that the empty matrix concept has utility only from a purely algebraic standpoint. Note, however, that determinants, eigenvalues, singular values, and norms of  empty matrices are considered in the current version of MATLAB."

Regards,
Rafael