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In determinant expansion by minors, the minimal number of transpositions of adjacent columns in a square matrix needed to turn the matrix representing a permutation of ...

Let ||A|| be the matrix norm associated with the matrix A and |x| be the vector norm associated with a vector x. Let the product Ax be defined, then ||A|| and |x| are said to ...

A diagonal of a square matrix which is traversed in the "northeast" direction. "The" skew diagonal (or "secondary diagonal") of an n×n square matrix is the skew diagonal from ...

The Sombor energy of a graph is defined as the graph energy of its Sombor matrix, i.e., the sum of the absolute values of the eigenvalues of its Sombor matrix.

A linear system of equations is a set of n linear equations in k variables (sometimes called "unknowns"). Linear systems can be represented in matrix form as the matrix ...

The Randić energy of a graph is defined as the graph energy of its Randić matrix, i.e., the sum of the absolute values of the eigenvalues of its Randić matrix.

The elliptic exponential function eexp_(a,b)(u) gives the value of x in the elliptic logarithm eln_(a,b)(x)=1/2int_infty^x(dt)/(sqrt(t^3+at^2+bt)) for a and b real such that ...

Infinite series of various simple functions of the logarithm include sum_(k=1)^^^inftylnk = 1/2ln(2pi) (1) sum_(k=1)^^^infty(-1)^klnk = 1/2ln(1/2pi) (2) ...

If X_i for i=1, ..., m has a multivariate normal distribution with mean vector mu=0 and covariance matrix Sigma, and X denotes the m×p matrix composed of the row vectors X_i, ...

The conjugate transpose of an m×n matrix A is the n×m matrix defined by A^(H)=A^_^(T), (1) where A^(T) denotes the transpose of the matrix A and A^_ denotes the conjugate ...