Homogeneity: T(c * u) = c * T(u) for any scalar c and vector u. Additivity: T(u + v) = T(u) + T(v) for any vectors u and v. The range of a linear transformation T is the set of all vectors that can be ...

This is a subject I struggled with the first time I took it. Ironically, this was the engineering version of it. It wasn't until I took the rigorous, axiomatic version that everything clicked.

direction with no spatial rotation (i.e., a Lorentz boost in the x direction). The Lorentz transformations are calculated here as linear transformations of four-vectors [ct, x, y, z] described by ...

The graph theory based approach to the three-body problem is introduced. Vectors of linear and angular momenta of the particles form the vertices of the graph. Scalar products of the vectors of the ...

Journal of the Royal Statistical Society. Series B (Statistical Methodology), Vol. 76, No. 2 (MARCH 2014), pp. 349-372 (24 pages) The paper considers in the high dimensional setting a canonical ...