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Every complex matrix can be broken into a Hermitian part A_H=1/2(A+A^(H)) (i.e., A_H is a Hermitian matrix) and an antihermitian part A_(AH)=1/2(A-A^(H)) (i.e., A_(AH) is an ...

A Hermitian inner product on a complex vector space V is a complex-valued bilinear form on V which is antilinear in the second slot, and is positive definite. That is, it ...

Given a system of two ordinary differential equations x^. = f(x,y) (1) y^. = g(x,y), (2) let x_0 and y_0 denote fixed points with x^.=y^.=0, so f(x_0,y_0) = 0 (3) g(x_0,y_0) ...

The Randić spectral radius rho_(Randic) of a graph is defined as the largest eigenvalue of its Randić matrix.

Let the elements in a payoff matrix be denoted a_(ij), where the is are player A's strategies and the js are player B's strategies. Player A can get at least min_(j<=n)a_(ij) ...

Let p and q be partitions of a positive integer, then there exists a (0,1)-matrix A such that c(A)=p, r(A)=q iff q is dominated by p^*.

A finite simple connected graph G is quadratically embeddable if its quadratic embedding constant QEC(G) is nonpositive, i.e., QEC(G)<=0. A graph being quadratically ...

Let P be a matrix of eigenvectors of a given square matrix A and D be a diagonal matrix with the corresponding eigenvalues on the diagonal. Then, as long as P is a square ...

The matrix decomposition of a square matrix A into so-called eigenvalues and eigenvectors is an extremely important one. This decomposition generally goes under the name ...

If A=(a_(ij)) is a diagonal matrix, then Q(v)=v^(T)Av=suma_(ii)v_i^2 (1) is a diagonal quadratic form, and Q(v,w)=v^(T)Aw is its associated diagonal symmetric bilinear form. ...