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Two matrices A and B which satisfy AB=BA (1) under matrix multiplication are said to be commuting. In general, matrix multiplication is not commutative. Furthermore, in ...

For every dimension n>0, the orthogonal group O(n) is the group of n×n orthogonal matrices. These matrices form a group because they are closed under multiplication and ...

The Epstein zeta function for a n×n matrix S of a positive definite real quadratic form and rho a complex variable with R[rho]>n/2 (where R[z] denotes the real part) is ...

The antipedal triangle DeltaA^'B^'C^' of a reference triangle DeltaABC with respect to a given point P is the triangle of which DeltaABC is the pedal triangle with respect to ...

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 vector space generated by the rows of a matrix viewed as vectors. The row space of a n×m matrix A with real entries is a subspace generated by n elements of R^m, hence ...

Fisher's exact test is a statistical test used to determine if there are nonrandom associations between two categorical variables. Let there exist two such variables X and Y, ...

Let A be an n×n matrix over a field F. Using the three elementary row and column operations over elements in the field, the n×n matrix xI-A with entries from the principal ...

Given an m×n matrix A, the fundamental theorem of linear algebra is a collection of results relating various properties of the four fundamental matrix subspaces of A. In ...

A dual number is a number x+epsilony, where x,y in R and epsilon is a matrix with the property that epsilon^2=0 (such as epsilon=[0 1; 0 0]).