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The identity matrix is a the simplest nontrivial diagonal matrix, defined such that I(X)=X (1) for all vectors X. An identity matrix may be denoted 1, I, E (the latter being ...

The trace of an n×n square matrix A is defined to be Tr(A)=sum_(i=1)^na_(ii), (1) i.e., the sum of the diagonal elements. The matrix trace is implemented in the Wolfram ...

A subset {v_1,...,v_k} of a vector space V, with the inner product <,>, is called orthonormal if <v_i,v_j>=0 when i!=j. That is, the vectors are mutually perpendicular. ...

The Pauli matrices, also called the Pauli spin matrices, are complex matrices that arise in Pauli's treatment of spin in quantum mechanics. They are defined by sigma_1 = ...

To find the motion of a rectangular membrane with sides of length L_x and L_y (in the absence of gravity), use the two-dimensional wave equation ...

Vizing's theorem states that a graph can be edge-colored in either Delta or Delta+1 colors, where Delta is the maximum vertex degree of the graph. A graph with edge chromatic ...

A quasi-regular graph is a graph such that degree of every vertex is the same delta except for a single vertex whose degree is Delta=delta+1 (Bozóki et al. 2020). ...

A hypergeometric class of orthogonal polynomials defined by R_n(lambda(x);alpha,beta,gamma,delta) =_4F_3(-n,n+alpha+beta+1,-x,x+gamma+delta+1; alpha+1,beta+delta+1,gamma+1;1) ...

The distribution parameter of a noncylindrical ruled surface parameterized by x(u,v)=sigma(u)+vdelta(u), (1) where sigma is the striction curve and delta the director curve, ...

If any set of points is displaced by X^idx_i where all distance relationships are unchanged (i.e., there is an isometry), then the vector field is called a Killing vector. ...