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__

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