In this article, we present what we believe to be a simple way to motivate the use of Hilbert spaces in quantum mechanics. To achieve this, we study the way the notion of dimension can, at a very primitive level, be defined as the cardinality of a maximal collection of mutually orthogonal elements (which, for instance, can be seen as spatial directions). Following this idea, we develop a formal...

A logic of orthogonality characterizes all “orthogonality consequences” of a given class Σ of morphisms, i.e. those morphisms s such that every object orthogonal to Σ is also orthogonal to s. A simple four-rule deduction system is formulated which is sound in every cocomplete category. In locally presentable categories we prove that the deduction system is also complete (a) for all classes Σ of...

The purpose of this paper is to introduce and discuss the concept of orthogonality in normed spaces. A concept of orthogonality on normed linear space was introduced. We obtain some subspaces of Banach spaces which are topologically complemented.

Multiple-input multiple-output (MIMO) radar has superior performance to conventional one. It has been introduced to almost every application field of conventional radar in recent years. In practical application, MIMO radar also faces the problem of congested spectrum assignment, which makes it not possible to have a continuous clear band with large bandwidth. Sparse frequency waveform that cont...

A multiparticle wavefunction, which is a solution of the multiparticle Schrödinger equation, satisfies the antisymmetry condition, thus making it natural to approximate it as a sum of Slater determinants. Many current methods do so but, in addition, they impose structural constraints on the Slater determinants, such as orthogonality between orbitals or a particular excitation pattern. By removi...