# BUAB

AcronymDefinition
BUABBuilt-Up Area Boundary (UK)
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A [{2}.sub.R(B),*] = {BU | [member of] [C.sup.kxm], BUAB = B}
(iv) There exist U [member of] [C.sup.kxm] and V [member of] [C.sup.nxl] such that BUAB = B, CAVC = C, and BU = VC.
by X = BU and B = BUAB = XAB it follows that R(X) = R(B), and by C = CAVC = CAX it follows that N(X) = N(C).
(ii) There exist U, X [member of] [C.sup.kxm] such that BUAB = B and ABVA = A.
for arbitrary [(AB).sup.(1)] [member of] (AB){1}, [(CA).sup.(1)] [member of] (CA){1}, and [(CAB).sup.(1)] [member of] (CAB){1} and arbitrary U [member of] [C.sup.kxm] and V [member of] [C.sup.nxl] satisfying BUAB = B and CAVC = C.
(b) Let U [member of] [C.sup.kxm] and V [member of] [C.sup.nxl] be arbitrary matrices satisfying BUAB = B and CAVC = C, and set X = BUAVC.
Namely, the problem of computing a {2}-inverse X of A satisfying R(X) = R(B) boils down to the problem of computing a solution to the matrix equation BUAB = B, where U is an unknown matrix taking values in [C.sup.kxm].
If it is satisfied, then the equation BUAB = B is solvable and we compute an arbitrary solution U to this equation, after which we compute a {2}-inverse X of A satisfying R(X) = ,R(B) as X = BU.
then the equations BUAB = B and CAVC = C are solvable, and we compute an arbitrary solution U to the first one and an arbitrary solution V of the second one.
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