22.1 Output notation for pseudoinverse and perp’s

P inv[x]     -→    x+       xx+x =  x,  x+xx+  =  x+,
                           (x+x)T  =  x+x,   (xx+)T =  xx+


P erpL[x]   -→    x⌊       x⌊x = 0

P erpR[x]   -→    x⌋       xx⌋ = 0

                   ⌊⌊        ⌊⌊         +      ⌊⌊ T     ⌊⌊
P erpL2[x]  -→    x        x  = 1 - xx  ,  (x )  = x

P erpR2[x]  -→    x⌋⌋       x⌋⌋ = 1 - x+x,   (x⌋⌋)T = x ⌋⌋

22.1.1 NCAddTranspose[aListOfExpressions]

Aliases:
Description: One can save time when working in an algebra with transposes or adjoints by using the command NCAddTranspose[ ]. These commands “symmetrize” a set of relations by applying tp[ ] to the relations and returning a list with the new expressions appended to the old ones. This saves the user the trouble of typing both a = b and tp[a] = tp[b].
Arguments: aListOfExpressions is a list of expressions
Comments / Limitations:

22.1.2 NCAddAdjoint[aListOfExpressions]

Aliases:
Description: One can save time when working in an algebra with transposes or adjoints by using the command NCAddAdjoint[ ]. These commands “symmetrize” a set of relations by applying aj[ ] to the relations and returning a list with the new expressions appended to the old ones. This saves the user the trouble of typing both a = b and aj[a] = aj[b].
Arguments: aListOfExpressions is a list of expressions
Comments / Limitations:

22.1.3 Pulling important equations into your session from an NCProcess output - See GetCategories in §23.0.5.

22.1.4 Help in typing Monomial Orders - See NCAutomaticOrder Section 18.4.6