2 citations · 2 across the 10 of their papers we have counts for
10 papers
A conjecture concerning *-algebras that unifies some matrix decompositions
Ran Gutin
In this note, we propose a simple-looking but broad conjecture about star-algebras over the field of real numbers. The conjecture enables many matrix decompositions to be represent…
An interactive visualisation for all 2x2 real matrices, with applications to conveying the dynamics of iterative eigenvalue algorithms
Ran Gutin
We present two interactive visualisations of 2x2 real matrices, which we call v1 and v2. v1 is only valid for PSD matrices, and uses the spectral theorem in a trivial way -- we use…
A Language for Evaluating Derivatives of Functionals Using Automatic Differentiation
Pietro Di Gianantonio, Abbas Edalat, Ran Gutin
We present a simple functional programming language, called Dual PCF, that implements forward mode automatic differentiation using dual numbers in the framework of exact real numbe…
Unitary canonical forms over Clifford algebras, and an observed unification of some real-matrix decompositions
Ran Gutin
We show that the spectral theorem -- which we understand to be a statement that every self-adjoint matrix admits a certain type of canonical form under unitary similarity -- admits…
A visualisation for conveying the dynamics of iterative eigenvalue algorithms over PSD matrices
Ran Gutin
We propose a new way of visualising the dynamics of iterative eigenvalue algorithms such as the QR algorithm, over the important special case of PSD (positive semi-definite) matric…
Towards a Singular Value Decomposition and spectral theory for all rings
Ran Gutin
We propose definitions of SVD, spectral decomposition (for self-adjoint matrices) and Jordan decomposition which make sense for all rings. For many rings, these decompositions can…
An analogue of the relationship between SVD and pseudoinverse over double-complex matrices
Ran Gutin
We present a generalisation of the pseudoinverse operation to pairs of matrices, as opposed to single matrices alone. We note the fact that the Singular Value Decomposition can be…
Matrix decompositions over the double numbers
Ran Gutin
We take matrix decompositions that are usually applied to matrices over the real numbers or complex numbers, and extend them to matrices over an algebra called the double numbers.…
Generalisations of Singular Value Decomposition to dual-numbered matrices
Ran Gutin
We present two generalisations of Singular Value Decomposition from real-numbered matrices to dual-numbered matrices. We prove that every dual-numbered matrix has both types of SVD…
Constructive proof of Herschfeld's Convergence Theorem
Ran Gutin
In this paper, we present a constructive proof of Herschfeld's Convergence Theorem. Our formulation differs from Herschfeld's in a few ways: We consider radicals that nest transfin…