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The Sherman-Morrison formula is a formula that allows a perturbed matrix to be computed for a change to a given matrix A. If the change can be written in the form u tensor v ...

Two square matrices A and B that are related by B=X^(-1)AX, (1) where X is a square nonsingular matrix are said to be similar. A transformation of the form X^(-1)AX is called ...

The order ideal in Lambda, the ring of integral laurent polynomials, associated with an Alexander matrix for a knot K. Any generator of a principal Alexander ideal is called ...

Two or more functions, equations, or vectors f_1, f_2, ..., which are not linearly dependent, i.e., cannot be expressed in the form a_1f_1+a_2f_2+...+a_nf_n=0 with a_1, a_2, ...

Proved in 1933. If q is an odd prime or q=0 and n is any positive integer, then there is a Hadamard matrix of order m=2^e(q^n+1), where e is any positive integer such that ...

A shortest path between two vertices of a graph is a graph path of shortest possible length between them. Such paths are also known as graph geodesics, and the matrix giving ...

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 ...