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Linear Transformations and Geometry

Published online by Cambridge University Press:  31 October 2008

James Hyslop
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The following note suggests certain connections between the theory of linear transformations and quadratic forms on the one hand, and the geometry of second degree surfaces on the other. It is hoped that the note may prove useful to those who may have to teach either theory to students who already possess an elementary knowledge of the other. The general ideas may be such as may well have occurred to anyone familiar with both theories, but the examples given may be new to readers.

Information

Type
Research Article
Information
Edinburgh Mathematical Notes , Volume 25 , January 1930 , pp. iv - x
Copyright
Copyright © Edinburgh Mathematical Society 1930

References

1 The relation cannot be of degree lower than the n th, as an application of the reciprocal transformation shows.

1 Cf. Frost: Solid Geometry (1886), p. 143.Google Scholar

1 We first make the principal axes of E the new axes of reference, then apply a transformation like (3) of § 2.

1 The line segments OA 1, OA 2, OA S form a right-handed triad, if the direction of rotation round the triangle A1A2A3 is clockwise, when viewed from O. By a convention, the positive directions of three Cartesian axes of reference form a right-handed triad, unless in exceptional cases.