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Messenger of Mathematics, Vol. 19

Excerpt from Messenger of Mathematics, Vol. 19 All the proofs that I am acquainted with (and their name is legion) of the possibility of depriving a quadric, in three or more variables, of its mixed terms by a real orthogonal transformation are made to depend on the theorem that the "latent roots" of any symmetrical matrix are all real. By the latent roots is understood the roots of the determinant expressed by tacking on a variable - to each term in the diagonal of symmetry to such matrix. I shall show that the same conclusion may be established a priori by purely algebraical ratiocination and without constructing any equation, by the method of cumulative variation. The proof I employ is inductive: i.e. if the theorem is true for two or any number of variables I prove that it will be true for one more. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works."
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