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Given a ring R with identity, the special linear group SL_n(R) is the group of n×n matrices with elements in R and determinant 1. The special linear group SL_n(q), where q is ...

A square matrix is said to be totally positive if the determinant of any square submatrix, including the minors, is positive. For instance, any 2×2 matrix whose determinant ...

An upper triangular matrix U is defined by U_(ij)={a_(ij) for i<=j; 0 for i>j. (1) Written explicitly, U=[a_(11) a_(12) ... a_(1n); 0 a_(22) ... a_(2n); | | ... |; 0 0 ... ...

A triangular matrix U of the form U_(ij)={a_(ij) for i<=j; 0 for i>j. (1) Written explicitly, U=[a_(11) a_(12) ... a_(1n); 0 a_(22) ... a_(2n); | | ... |; 0 0 ... a_(nn)]. ...

An additive cellular automaton is a cellular automaton whose rule is compatible with an addition of states. Typically, this addition is derived from modular arithmetic. ...

To predict the result of a measurement requires (1) a model of the system under investigation, and (2) a physical theory linking the parameters of the model to the parameters ...

Abstract Algebra

An n-Hadamard graph is a graph on 4n vertices defined in terms of a Hadamard matrix H_n=(h)_(ij) as follows. Define 4n symbols r_i^+, r_i^-, c_i^+, and c_i^-, where r stands ...

A transpose of a doubly indexed object is the object obtained by replacing all elements a_(ij) with a_(ji). For a second-tensor rank tensor a_(ij), the tensor transpose is ...

The graph distance matrix, sometimes also called the all-pairs shortest path matrix, is the square matrix (d_(ij)) consisting of all graph distances from vertex v_i to vertex ...