This construction is reversible, and the incidence matrix of a symmetric 2-design with these parameters can be used to form an Hadamard matrix of order 4 " a ".
22.
The reason for this is that A can be written as A = J J ^ T-2I, where J is the signless incidence matrix of the pre-line graph and I is the identity.
23.
However, this pool of items can be reduced to form the "'reduced incidence matrix "'( Q r ), by imposing the constraints of the attribute hierarchy as defined by the R matrix.
24.
Thus, for most purposes it makes no difference which orientation we use to define the incidence matrix, and we may speak of "'the "'incidence matrix of ? without worrying about exactly which one it is.
25.
Thus, for most purposes it makes no difference which orientation we use to define the incidence matrix, and we may speak of "'the "'incidence matrix of ? without worrying about exactly which one it is.
26.
This allows techniques from matrix algebra to be applied, " e . g . " that the trace of a matrix is log of the determinant, with the matrix representation of a graph arising from the graph's incidence matrix.
27.
The "'incidence matrix "'of a ( finite ) incidence structure is a matrix with entries 0 or 1 that has its rows indexed by the points } and columns indexed by the lines } where the ij-th entry is a 1 if and 0 otherwise.
28.
Another extension is when the set of potential differences W _ { k } is from one network and the set of currents F _ { k } is from an entirely different network, so long as the two networks have the same topology ( same incidence matrix ) Tellegen's theorem remains true.
29.
If M is the inclusion matrix ( or incidence matrix of the Bratteli diagram ) of finite-dimensional semisimple ( complex ) algebras B and A, the depth two condition on the subalgebra B in A is given by an inequality MM ^ tM \ leq nM for some positive integer n ( and each corresponding entry ).
30.
But there is still a simple entity-relation ( beside the generalised Euler formulae for the diagonal, respectively the sub-diagonal entities of each row, respectively the super-diagonal elements of each row-those at least whenever no holes or stars etc . are considered ), as for any such incidence matrix I = ( I _ { ij } ) holds:
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