Affine Maps, Euclidean Motions and Quadrics by Agustí Reventós Tarrida

Author:Agustí Reventós Tarrida
Language: eng
Format: epub, pdf
Publisher: Springer London, London

where, by Proposition 2.28, or .

In both cases, the first vector of the basis, e 1, is an eigenvector of with eigenvalue 1, which can be taken (modifying if necessary the initial basis) as the normalized glide vector, that is, we can always select the above basis so that u f =de 1.

Since , in the first case () we have:

and in the second case () we have:

In summary, there always exists an orthonormal affine frame in which the matrix of f coincides with one of the matrices in the list of canonical expressions. This completes the proof. □

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