Minkowski Geometric Algebra of Complex Sets

Solution of elementary equations in the Minkowski geometric algebra of complex sets

m-Projections involving Minkowski inverse and range symmetric property in Minkowski space

In this paper we study the impact of Minkowski metric matrix on a projection in the Minkowski Space M along with their basic algebraic and geometric properties.The relation between the m-projections and the Minkowski inverse of a matrix A in the minkowski space M is derived. In the remaining portion commutativity of Minkowski inverse in Minkowski Space M is analyzed in terms of m-projections as...

Antisymmetric Matrices are Real Bivectors

This paper briefly reviews the conventional method of obtaining the canonical form of an antisymmetric (skewsymmetric, alternating) matrix. Conventionally a vector space over the complex field has to be introduced. After a short introduction to the universal mathematical “language” Geometric Calculus, its fundamentals, i.e. its “grammar” Geometric Algebra (Clifford Algebra) is explained. This l...

Minkowski Algebra I: a Convolution Theory of Closed Convex Sets and Relatively Open Convex Sets∗

This is the first one of a series of papers on Minkowski algebra. One of purposes of this paper is to set up a general framework so that the mixed volume theory and integral geometry can be developed algebraically in subsequent papers. The so called Minkowski algebra of convex sets is the vector space generated by indicator functions of closed convex sets and relatively open convex sets, where ...

On a Brunn-minkowski Theorem for a Geometric Domain Functional Considered by Avhadiev

Suppose two bounded subsets of IR are given. Parametrise the Minkowski combination of these sets by t. The Classical BrunnMinkowski Theorem asserts that the 1/n-th power of the volume of the convex combination is a concave function of t. A Brunn-Minkowski-style theorem is established for another geometric domain functional.