The loss value of multilinear regression
Determinant formulas are presented for: a certain positive semidefinite, hermitian matrix; the loss value of multilinear regression; the multiple linear regression coefficient.
stat.OT↗
arXiv subjects
Helmut Kahl
Publications and source records attributed to Helmut Kahl.
On the final limit of a transition matrix
An efficient algorithm is presented for computation of the limit of exp(t A) for t towards infinity where A denotes an intensity matrix of finite dimension.
math.CA↗
Symmetric Matrices: Theory and Applications
This text is a survey on symmetric matrices. It serves as a script for a module to be taught at university.
math.HO↗
Measuring quadric sectors at centre
Sectors at centre of affine quadrics with point symmetry are investigated over arbitrary fields of characteristic different from two. As an application we demonstrate nice formulas for the area and the volume of such planar and spatial sectors, respectively, in euclidean space. It seems that up to now there has been atmost little research in this field up to very special cases.
math.MG↗
An euclidean affine invariant of quadrilaterals
A certain real number, depending on two neighbouring sides of a quadrilateral and the diagonal meeting these two sides at their common point, is shown to be invariant under affinity. As an application we demonstrate a nice formula for the area of a finite sector at centre of a planar quadric with point symmetry.
math.GM↗
The area of a sector at centre of a planar quadric
Three linearly dependent and pairwise linearly independent vectors of an euclidian space uniquely determine a planar quadric with symmetry centre in the origin. A rather simple formula for the area of an arbitrary sector at centre of such a quadric will be shown by classical methods. The formula describes that area in dependence of 1. the lengths of the two straight lines that bound the sector at two sides, 2. the length of an arbitrary straight line from the centre to the quadric arc that bounds the sector at the third side, 3. the two angles in between these three straight lines.
math.HO↗