Unit-free transformations of linear relativity

Turns and Special Relativity Transformations

We advance an universal approach to the construction of kinematics in non-inertial and, in particular, rotating reference frames. On its basis, a 10-dimensional space including three projections of velocity vector and three turn angles in geometric space as additional coordinates to time and geometric coordinates is introduced. In a specific case, the turns in 10-space describe the uniform rota...

On One-Sided Ideals of Rings of Linear Transformations

Unit 3 Image Transformations

Introduction: Two dimensional unitary transforms play an important role in image processing. The term image transform refers to a class of unitary matrices used for representation of images. In analogy with I-D signals that can be represented by an orthogonal series of basis functions, we can similarly represent an image in terms of a discrete set of basis arrays called “basis images ". These a...

Linear Transformations

The n×m matrix AT obtained by exchanging rows and columns of A is called the transpose of A. A matrix A is said to be symmetric if A = AT . The sum of two matrices of equal size is the matrix of the entry-by-entry sums, and the scalar product of a real number a and an m× n matrix A is the m× n matrix of all the entries of A, each multiplied by a. The difference of two matrices of equal size A a...

Special Relativity and Linear Algebra

Before Einstein’s publication in 1905 of his theory of special relativity, the mathematical manipulations that were a product of his theory were in fact already known. The so called Lorentz transformations were tricks that had been found that allowed the speed of light to propagate in all directions at the same speed, which accounted for its strange behavior when traveling through the now infam...