| The $n$-dimensional pseudospheres are the surfaces in ${bf R}^{n+1}$ given by the equations ${x_1}^2+{x_2}^2+ ldots {x_k}^2-{x_{k+1}}^2- cdots - {x_{n+1}}^2=1$ ($1 leq k leq n+1$). We consider the pseudospheres as surfaces in $E_{n+1,k}$, where $E_{m,k}={bf R}^k times {(i{bf R})}^{m-k}$, and investigate their geometry in terms of the linear algebra of these spaces. Each of the spaces $E_{m,k}$ has a natural (not generally positive definite) metric, which is inherited by the pseudospheres. We prove that each matrix with columns in $E_{m,k}$ can be put into a canonical form by premultiplying by an orthogonal matrix (a matrix which effects an isometry of $E_{m,k}$). We term a matrix in this form {em bitriangular}. This generalizes upper triangular form for real square matrices. |
Keywords
Math Review Classification
Primary 15A21, 51M10
Last Updated
21/3/97
Length
21 pages
Availability
This article is available in: