For any matrix W [member of] [??] there exists a unimodular matrix
U [member of] [??] such that U x Wis in the Popov form.
Different basis can be transferred by a unimodular matrix
whose determinant is [+ or -]1 and each matrix element is an integer.
The unimodular matrix
which represents these operations
The recent work Su and Wagner  defines cuts and flows of a regular matroid (i.e., one represented by a totally unimodular matrix
M); when M is the boundary matrix of a cell complex, this is the case where the torsion coefficients are all trivial.
For an unimodular matrix
 the following expression is verified:
It is a basic concept of lattice theory that if T is an unimodular matrix
then B and [B.sup.new] span the same lattice.
The matrix A' is the incidence matrix of the edge-triangle graph underlying the given triangulation, and, then [31, 12] the matrix A' is a totally unimodular matrix
and has rank [N.sub.T].
[m.sub.Y], that form a basis for Ker([Pi]), and which can be unimodularly(4) completed (i.e., there exists an [n.sub.Y] x [n.sub.Y] unimodular matrix
, my of whose columns are [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
Two polynomial matrices P [element of] [R.sup.m x n][s] and R [element of] [R.sup.m x n][s] are called unimodularly equivalent if there exists a unimodular matrix
U [element of] [R.sup.n x n][s] such that PU = R.
Under the assumption that the matrix P, related closely to P, is in the row-reduced form (and respective i/o equations are in the strong row-reduced form), P will be transformed into the Popov form, multiplying from the left by a certain unimodular matrix
. Then the obtained unimodular transformation matrix is applied to the original system equations.
At last, since the unimodular matrix
, which is derived by LR algorithm, may be dependent on the CSI quality, this paper also investigates the impact of imperfect CSI and channel asymmetry in the simulation.
The Ehrhart polynomial of a zonotope that is defined by a totally unimodular matrix
is also an evaluation of the Tutte polynomial (see e.