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The ABC (atom-bond connectivity) matrix A_(ABC) of a simple graph is a weighted adjacency matrix with weight f(d_i,d_j)=sqrt((d_i+d_j-2)/(d_id_j)), (1) where d_i are the ...

The arithmetic-geometric matrix A_(AG) of a simple graph is a weighted adjacency matrix with weight f(d_i,d_j)=sqrt(d_i^2+d_j^2), (1) where d_i are the vertex degrees of the ...

The characteristic equation is the equation which is solved to find a matrix's eigenvalues, also called the characteristic polynomial. For a general k×k matrix A, the ...

The eigenvector corresponding to the second smallest eigenvalue (i.e., the algebraic connectivity) of the Laplacian matrix of a graph G. The Fiedler vector is used in ...

The energy of a graph is defined as the sum of the absolute values of its graph eigenvalues (i.e., the sum of its graph spectrum terms). Other varieties of graph energy are ...

The invertible matrix theorem is a theorem in linear algebra which gives a series of equivalent conditions for an n×n square matrix A to have an inverse. In particular, A is ...

The Jordan canonical form, also called the classical canonical form, of a special type of block matrix in which each block consists of Jordan blocks with possibly differing ...

The Laplacian spectral radius of a finite graph is defined as the largest value of its Laplacian spectrum, i.e., the largest eigenvalue of the Laplacian matrix (Lin et al. ...

Consider a collection of diagonal matrices H_1,...,H_k, which span a subspace h. Then the ith eigenvalue, i.e., the ith entry along the diagonal, is a linear functional on h, ...

The Montgomery-Odlyzko law (which is a law in the sense of empirical observation instead of through mathematical proof) states that the distribution of the spacing between ...