Thesis (Ph. D.)--University of Chicago, 1920. / "Private edition distributed by the University of Chicago Libraries." "Reprinted from Transactions of the American mathematical society, volume 22, number 1 (January, 1921)."

[No abstract submitted] / Science, Faculty of / Mathematics, Department of / Graduate

Let A be an n x n hermitian matrix, let E₂(a₁, …, a_k) be the second elementary symmetric function of the letters a₁, …, a_k and let C₂(A) be the second compound matrix of A. In this thesis the maximum and minimum of det {(Ax_█, x_j)} and E₂ [(Ax₁, x₁), …, (Ax_█(k@), x_k)] the minimum of [formula omitted] (C₂(A)x_i ₁⋀x_i₂ , x_i₁ ⋀ax_i₂) are calculated. The maxima and minima are taken over all sets of k orthonormal vectors in unitary n-space and x_█(i@)₁ ⋀ x_i ₂ designates the Grassman exterior product. These results depend on the inequality E₂(a₁, …, a_k ) ≤ (k/2 ) [formula omitted] which is here established for arbitrary real numbers, and on the minimum of E₂ (x₁, …, x_(k)) where the minimum is taken over all values of x₁, …, x_█(k@) such that ∑_(i=1)^k▒xi = ∑_(i=1)^k▒〖∝i〗 and ∑_(i=1)^q▒xsi ≤ ∑_(i=1)^q▒〖∝i〗 for all sets of q distinct integers s₁, …, s_q taken from 1, …, k. Here α₁ ≥ … ≥ ∝_k. / Science, Faculty of / Mathematics, Department of / Graduate

"The object of this paper is to present a detailed, illustrated discussion of a portion of the theory of bilinear forms as found in Volume 2 of Lectures in Abstract Algebra by Nathan Jacobson. This theory involves the fundamental properties of bilinear forms on finite dimensional vector spaces over arbitrary division rings and includes such things as a discussion of the relationship between matrices and bilinear forms as well as the definition of the transpose of a transformation relative to a pair of bilinear forms; a definition independent of the matrix representations of the forms"--Introduction. / Typescript. / "May, 1955." / "Submitted to the Graduate Council of Florida State University in partial fulfillment of the requirements for the degree of Master of Science." / Advisor: Nickolas Heerema, Professor Directing Paper. / Includes bibliographical references (leaf 30).

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In this thesis, we introduce a new space of Hermitian Jacobi forms, and we determine its structure. As an application, we study heat cycles of Hermitian Jacobi forms, and we establish a criterion for the existence of U(p) congruences of Hermitian Jacobi forms. We demonstrate that criterion with some explicit examples. Finally, in the appendix we give tables of Fourier series coefficients of several Hermitian Jacobi forms.

Typescript, etc. / Digitized by Kansas State University Libraries