The size r + 1 square matrix above is obtained by choosing r + 1 such rows in all possible ways and taking determinants.
On Resolving Singularities
The template class Matrix represents a square matrix with arbitrary rank, where the rank plays the role of the template parameter.
AMEGIC++ 1.0, A Matrix Element Generator In C++
Every real square matrix Π satisfying these conditions is called stochastic.
The temporal calculus of conditional objects and conditional events
Consider a square matrix B of size N containing non-negative entries.
Random unistochastic matrices
It is a square matrix of size V whose matrix elements Ci,j take the values 1 if the vertices i, j are connected with a bond, or 0 otherwise.
Statistical properties of resonance widths for open Quantum Graphs
Finally, for any invertible square matrix a we denote by a−t the transpose of a−1 .
Non-commutative Polynomials of Independent Gaussian Random Matrices. The Real and Symplectic Cases
To do so we ﬁrst expand the squared matrix elements of O in terms of the perturbation parameter λ.
A random matrix formulation of fidelity decay
Let M be a square matrix with coeﬃcients say Mi,j .
Measure convolution semigroups and non-infinitely divisible probability distributions
As for A3 , A8 , and the electromagnetic ﬁeld Aγ , on the other hand, mixing between them arises and thus we have to refer to eigenvalues of the 3 × 3 mass squared matrix to investigate instability.
Analytical and numerical evaluation of the Debye and Meissner masses in dense neutral three-flavor quark matter
In the symmetric CFL state with Ms = 0, the mass squared matrix is diagonal in color and all eight gluons have the same screening mass.
Analytical and numerical evaluation of the Debye and Meissner masses in dense neutral three-flavor quark matter
We denote the normalized trace of a square matrix X by tr X (whatever the size of X is).
Rectangular random matrices. Related convolution
We call a square matrix zero-diagonal if it has only zeros on the main diagonal; let ZD(n) be the space (Lie algebra if p = 2) of symmetric zero-diagonal n × n-matrices.
Non-degenerate bilinear forms in characteristic 2, related contact forms, simple Lie algebras and superalgebras
The Laplacian of an undirected graph is a square matrix, whose eigenvalues yield important information.
Laplacians on shifted multicomplexes
Mi )2 = det(M T M ), where Mi stands for the square matrix obtained from M by deleting the i-th row.
Average volume, curvatures, and Euler characteristic of random real algebraic varieties
Mt ∈ Rd and Ct is a symmetric, positive deﬁnite square matrix.
The size of random fragmentation trees
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