To do so first consider the elements cci, i= 1, 2,***, a; j= 1, 2,---, f. Equations (6) are evidently
satisfied for every cij where ai and bj are relatively prime. If ai and bj have the greatest …

1. Introduction. Interest in qualitative problems in matrix theory has been stimulated by the
desireto solve certain problems inmathematical economics. Yet it seems clear that the …

Matric algebra is a mathematical abstraction underlying many seemingly diverse theories.
Thus bilinear and quadratic forms, linear associative algebra (hypercomplex systems), linear …

The term matrix might be used in a more general sense, but in the present memoir I consider
only square and rectangular matrices, and the term matrix used without qualification is to be …

The elementary theorems of the classical treatment of symmetric and alternate matrices may
be shown, without change in the proofs, to hold for matrices whose elements are in any field …

THEOREM 2. Let A, B be a pair of matrices with property D. Assume that no matrix XA+, MB
(for X, y O, 0) in the pencil has a characteristic root of multiplicity_3 nor two different double …

Let C be a square matrix with complex elements. If C= C'(C'denotes the transpose of C)
there exists a unitary matrix U such that (1) where the μ's are the non-negative square roots …

1. Introduction. Let Sm denote the symmetric group of degree m and let H be a subgroup of
Sm of order h. Let x be a character of degree 1 on H, ie, a nontrivial homomorphism of H into …

The matrix elements vi of to the following laws:(a) The distribution Pij (Vij) of the vi for i< j are
independent. In other words, there are no statistical correlations between the matrix ele …

1. It was proved by Frobenius [1] that any function f (A, B) of two commutative n Xn square
matrices A, B has as characteristic roots the numbers f (Xi,/ui) where Xi are the characteristic …