In the case of determinate systems, matrix b is square and the solution for Q can be found immediately from (3) provided that the system is stable.

Already for there exist a bistochastic matrix B which is not unistochastic:

The parenthesized expressions define a matrix B relating the internal and external modes to the displacements.

In the case of a statically indeterminate system, matrix B is not unique because the set of that satisfies nodal equilibrium is infinite.

Clearly, the matrix B uniquely represents the bipartite graphs.

The biadjacency matrix is the r x s 0-1 matrix B in which iff .

The function , where is the determinant of a nonnegative-definite matrix B, is concave.

In the general case the matrix B is a numerical quantity containing information on the geometry of the chosen mesh.

Now consider the matrix B, which yields two equal eigenvalues but simple degeneracy.

Input coupling matrix B has a non-zero gain term as its last element if vector u is non-zero.