Document Type

Research

Abstract

Let x denote the real n-tuple (x₁,…,x_n), (xx… ) the iterated n-tuple (x₁,…,x_n,x₁,…x_n…), A = (a i j) and A' a square matrix and its transpose. We wish to consider the effect of nonsingular transformations on a sum x(A₁, + ... + A_k)x' of k quadratic forms when the real symmetric matrices A_i and A = A, + ... + A_k are subjected to certain restrictions on their ranks. The results attained link a theorem in statistics with a theorem in ring theory (see Corollary 3). Extension of the results to hermitean forms follows easily.

Publication Date

1948

Journal Title

Proceedings of the Iowa Academy of Science

Volume

Issue

First Page

291

Last Page

292

Copyright

Language

File Format

application/pdf

Recommended Citation

Vinograde, B. (1948) "Simultaneous Reduction of Quadratic Forms," Proceedings of the Iowa Academy of Science, 55(1), 291-292.
Available at: https://scholarworks.uni.edu/pias/vol55/iss1/39

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Simultaneous Reduction of Quadratic Forms

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