Simple image set of linear mappings in a max–min algebra

Simple image set of linear mappings in a max-min algebra

For a given linear mapping, determined by a square matrix A in a max–min algebra, the set SA consisting of all vectors with a unique pre-image (in short: the simple image set of A) is considered. It is shown that if the matrix A is generally trapezoidal, then the closure of SA is a subset of the set of all eigenvectors of A. In the general case, there is a permutation , such that the closure of...

Set Theory in Linear Algebra

Set theory language is an essential prerequisite for the cognition of linear algebra concepts. Many difficulties of cognition in linear algebra may be explained by the lack of mastery of set theory concepts. In the paper, an in depth discussion of documented categories of difficulties originated from set theory is provided.

Image Feature Set for Correspondence Mappings

We present a method to automatically construct features capable of putting images in correspondence with each other (i.e., registration) without requiring control points or landmarks on the images in question. Our method is based primarily on Principal Component Analysis (PCA) and a suitable image representation. The feature set is a collection of weight vectors and the correspondence mapping i...

An Updated Set of Basic Linear Algebra

Conformal Mappings in Geometric Algebra

I n 1878 William Kingdon Clifford wrote down the rules for his geometric algebra, also known as Clifford algebra. We argue in this paper that in doing so he laid down the groundwork that is profoundly altering the language used by the mathematical community to express geometrical ideas. In the real estate business everyone knows that what is most important is location. We demonstrate here that ...