In this expository paper, we present a new and easier proof of the Polar Decomposition Theorem. Unlike in classical proofs, we do not use the square root of a positive matrix. The presented proof is accessible to a broad audience.
The aim of the paper is to present results concerning the ρ-orthogonality and its preservation (both accurate and approximate) by linear operators. We survey on the results presented in [11] and [23], as well as give some new and more general ones.
In this paper we consider the approximate orthogonalities in real normed spaces. Using the notion of approximate orthogonalities in real normed spaces, we provide some new characterizations of rotundity and smoothness of dual spaces.
In the present paper, we give the exact solutions of a singular equation with logarithmic singularities in two classes of functions and construct formulae for the approximate solutions.
In the present paper, we give the exact solutions of a singular equation with logarithmic singularities in two classes of functions and construct formulae for the approximate solutions.
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