7 citations · 37 across the 15 of their papers we have counts for
15 papers
Enumeration of the New Plücker-like Equations
André L. G. Mandolesi
We give a more detailed description of the new system of Plücker-like equations from [4], discuss how it relates to the usual Plücker equations, and correct a mistake in that artic…
The Thousand Faces of Pythagoras (As Mil Faces de Pitágoras)
André L. G. Mandolesi
The Pythagorean Theorem is one of the oldest, more famous and more useful theorems of Mathematics, and possibly the one that has had the most impact in the evolution of this and ot…
Hermitian Geometry of Complex Multivectors, Determinants and Orientations
André L. G. Mandolesi
Two geometric interpretations for complex multivectors and determinants are presented: a little known one in terms of square roots of volumes, and a new one using fractions of volu…
Multivector Contractions Revisited, Part II
André L. G. Mandolesi
The theory of contractions of multivectors, and star duality, was reorganized in a previous article, and here we present some applications. First, we study inner and outer spaces a…
Asymmetric Geometry of Total Grassmannians
André L. G. Mandolesi
Metrics in Grassmannians, or distances between subspaces of same dimension, have many uses, and extending them to the Total Grassmannian of subspaces of different dimensions is an…
Asymmetric Metrics on the Full Grassmannian of Subspaces of Different Dimensions
André L. G. Mandolesi
Metrics on Grassmannians have a wide array of applications: machine learning, wireless communication, computer vision, etc. But the available distances between subspaces of distinc…
Multivector Contractions Revisited, Part I
André L. G. Mandolesi
We reorganize, simplify and expand the theory of contractions or interior products of multivectors, and related topics like Hodge star duality. Many results are generalized and new…
Grassmann angle formulas and identities
André L. G. Mandolesi
Grassmann angles improve upon similar concepts of angle between subspaces that measure volume contraction in orthogonal projections, working for real or complex subspaces, and bein…
Blade Products and the Angle Bivector of Subspaces
André L. G. Mandolesi
Principal angles are used to define an angle bivector of subspaces, which fully describes their relative inclination. Its exponential is related to the Clifford geometric product o…
Grassmann angles between real or complex subspaces
André L. G. Mandolesi
The Grassmann angle improves upon similar angles between subspaces that measure volume contraction in orthogonal projections. It works in real or complex spaces, with important dif…
Quantum fractionalism: the Born rule as a consequence of the complex Pythagorean theorem
André L. G. Mandolesi
Everettian Quantum Mechanics, or the Many Worlds Interpretation, lacks an explanation for quantum probabilities. We show that the values given by the Born rule equal projection fac…
Projection factors and generalized real and complex Pythagorean theorems
André L. G. Mandolesi
Projection factors describe the contraction of Lebesgue measures in orthogonal projections between subspaces of a real or complex inner product space. They are connected to Grassma…
Analysis of Wallace's Proof of the Born Rule in Everettian Quantum Mechanics II: Concepts and Axioms
André L. G. Mandolesi
Having analyzed the formal aspects of Wallace's proof of the Born rule, we now discuss the concepts and axioms upon which it is built. Justification for most axioms is shown to be…
Everettian Decoherent Histories and Causal Histories
André L. G. Mandolesi
D. Wallace has tried to use decoherence to solve the preferred basis problem of Everettian Quantum Mechanics, and this solution lays the foundation for his proof of the Born rule.…
Analysis of Wallace's Proof of the Born Rule in Everettian Quantum Mechanics: Formal Aspects
André L. G. Mandolesi
To solve the probability problem of the Many Worlds Interpretation of Quantum Mechanics, D.Wallace has presented a formal proof of the Born rule via decision theory, as proposed by…