Elements of Vector Algebra

A vector needs an arithmetic of its own, and Ludwik Silberstein set the whole of it down in barely forty pages – an introduction written in 1919 and still hard to better.

Elements of Vector Algebra was written by the Polish physicist Ludwik Silberstein (1872–1948) at the request of the instrument makers Adam Hilger, as a companion to his Simplified Method of Tracing Rays of 1918. His aim was to give people working in geometrical optics exactly what they needed and nothing more, so the critical subtleties are set aside in favour of clear definition and immediate use – though he hoped, as he says in his preface, that it would also serve anyone coming to the subject fresh.

The argument builds from the definition of a vector through addition and subtraction to the scalar and vector products, the expansion of vector formulae, the linear operator, and a closing chapter of hints on differentiation. Silberstein taught natural philosophy at Rome, later advised Eastman Kodak, and was among the physicists who carried vector and quaternion methods into relativity; he writes here like a man who expects the reader to start using the method the same afternoon.

This edition features:

• Silberstein's 1919 text, from the definition of a vector through to the linear operator
• Scalar and vector products explained with their geometric meaning made plain
• A closing chapter of hints on the differentiation of vectors
• Written as a companion to the author's own work on ray tracing in geometrical optics
• A short, self-contained start for anyone meeting vector methods for the first time