Matrix algebra
View article: Robust Stability of Linear Time Invariant Systems Represented by an Interval Matrix
Robust Stability of Linear Time Invariant Systems Represented by an Interval Matrix Open
This technical note summarizes the main results of the paper presented at the IEEE Conference on Control of Oscillations and Chaos (COC’97), where we proposed sufficient conditionsto guarantee the robust stability of linear time invariant …
View article: Structure Algebra III: Layer Reversion and the Structural Count
Structure Algebra III: Layer Reversion and the Structural Count Open
memo
View article: Linear Algebra
Linear Algebra Open
View article: Linear Algebra
Linear Algebra Open
View article: Structure Algebra II: The Structural Triangle Scalar Σ = mΛ in Boundary Hydrodynamic Structure Theory
Structure Algebra II: The Structural Triangle Scalar Σ = mΛ in Boundary Hydrodynamic Structure Theory Open
memo
View article: Robust Stability of Interval Matrices Applied to Circuit Systems Technical Summary for Open Dissemination
Robust Stability of Interval Matrices Applied to Circuit Systems Technical Summary for Open Dissemination Open
This technical note summarizes the main results of the paper presented at the IEEE Conference on Control of Oscillations and Chaos (COC’97), where we proposed sufficient conditionsto guarantee the robust stability of linear time invariant …
View article: Robust Stability Bounds for Interval Matrices in Circuit Design Technical Summary for Open Dissemination
Robust Stability Bounds for Interval Matrices in Circuit Design Technical Summary for Open Dissemination Open
This technical summary presents the core contributions of the paper presented at the 1997European Conference on Circuit Theory and Design (ECCTD’97), where we introduced simple and efficient tests for robust stability of electronic systems…
View article: Robust Stability Analysis of Interval Matrices in Control Applications Technical Summary for Open Dissemination
Robust Stability Analysis of Interval Matrices in Control Applications Technical Summary for Open Dissemination Open
This technical summary presents the main contributions of the paper accepted and presentedat Control ’97, held in Sydney, Australia. The work focused on robust stability analysis oflinear time invariant systems represented by interval matr…
View article: Robust Stability of Interval Matrices: Extended Applications in Circuit Theory Technical Summary for Open Dissemination
Robust Stability of Interval Matrices: Extended Applications in Circuit Theory Technical Summary for Open Dissemination Open
This technical summary presents the main contributions of the paper presented at the 1999European Conference on Circuit Theory and Design (ECCTD’99), held in Stresa, Italy.Building upon earlier results from ECCTD’97 and COC’97, we extended…
View article: QAv2/qualia-algebra: Qualia Algebra v2.0.1
QAv2/qualia-algebra: Qualia Algebra v2.0.1 Open
Revised papers + all figures uploaded
View article: JGR-NMF: joint graph-regularized non-negative matrix factorization for spatial domain identification
JGR-NMF: joint graph-regularized non-negative matrix factorization for spatial domain identification Open
Codes and datasets for JGR-NMF.
View article: JGR-NMF: joint graph-regularized non-negative matrix factorization for spatial domain identification
JGR-NMF: joint graph-regularized non-negative matrix factorization for spatial domain identification Open
Codes and datasets for JGR-NMF.
View article: Some functional identities characterizing two-sided centralizers and two-sided generalized derivations on triangular algebras
Some functional identities characterizing two-sided centralizers and two-sided generalized derivations on triangular algebras Open
Let T be a unital triangular algebra, let n > 1 be an integer, let gamma be an invertible element of Z(T), the center of T, and let Psi, Omega:\mathcal{T}\rightarrow \mathcal{T}$ be additive mappings satisfying \begin{align*} Ψ(X^n) = γX^{…
View article: Stable equivalences and homological dimensions
Stable equivalences and homological dimensions Open
As is known, every finite-dimensional algebra over a field is isomorphic to the centralizer algebra of two matrices. So it is fundamental to study first the centralizer algebra of a single matrix, called a centralizer matrix algebra. In th…
View article: The Tripartite Algebra of Coherence: T₇, anti-T₇ and the Monstrous Algebra as a Unified Structure
The Tripartite Algebra of Coherence: T₇, anti-T₇ and the Monstrous Algebra as a Unified Structure Open
This work introduces the Tripartite Algebra of Coherence, a unified mathematical-ontological framework composed of the T₇ algebra (positive regime), the anti-T₇ algebra (negative regime), and the Monstrous algebra (reciprocal deformation r…
View article: On the left and right coefficients of the general Cayley-Hamilton identities for an nxn matrix
On the left and right coefficients of the general Cayley-Hamilton identities for an nxn matrix Open
An nxn matrix A over an arbitrary unitary ring R satisfies invariant left and right Cayley-Hamilton identities with matrix coefficients C(i), D(i) having commutator sum entries. If R has a grading similar to the case of Grassmann algebras,…
View article: Hermitian Spectral Bound: Democratizing Robust Stability Analysis Through O(n 3 ) Real-Time Algebraic Validation
Hermitian Spectral Bound: Democratizing Robust Stability Analysis Through O(n 3 ) Real-Time Algebraic Validation Open
Robust stability validation traditionally relies on computationally expensive methods—Linear Matrix Inequalities (LMIs), μ-analysis, vertex enumeration—with O(n⁶) complexity, rendering them impractical for real-time embedded systems, large…
View article: Stable equivalences and homological dimensions
Stable equivalences and homological dimensions Open
As is known, every finite-dimensional algebra over a field is isomorphic to the centralizer algebra of two matrices. So it is fundamental to study first the centralizer algebra of a single matrix, called a centralizer matrix algebra. In th…
View article: On the left and right coefficients of the general Cayley-Hamilton identities for an nxn matrix
On the left and right coefficients of the general Cayley-Hamilton identities for an nxn matrix Open
An nxn matrix A over an arbitrary unitary ring R satisfies invariant left and right Cayley-Hamilton identities with matrix coefficients C(i), D(i) having commutator sum entries. If R has a grading similar to the case of Grassmann algebras,…
View article: Hermitian Spectral Bound: Democratizing Robust Stability Analysis Through O(n 3 ) Real-Time Algebraic Validation
Hermitian Spectral Bound: Democratizing Robust Stability Analysis Through O(n 3 ) Real-Time Algebraic Validation Open
Robust stability validation traditionally relies on computationally expensive methods—Linear Matrix Inequalities (LMIs), μ-analysis, vertex enumeration—with O(n⁶) complexity, rendering them impractical for real-time embedded systems, large…
View article: Quaternion Autocontained Framework (QAF)
Quaternion Autocontained Framework (QAF) Open
The complete description of reality in one page. The QAF is the most minimal, self-contained, and predictive theory ever proposed. Zero free parameters. No Big Bang, no inflation, no dark matter…
View article: Some functional identities characterizing two-sided centralizers and two-sided generalized derivations on triangular algebras
Some functional identities characterizing two-sided centralizers and two-sided generalized derivations on triangular algebras Open
Let T be a unital triangular algebra, let n > 1 be an integer, let gamma be an invertible element of Z(T), the center of T, and let Psi, Omega:\mathcal{T}\rightarrow \mathcal{T}$ be additive mappings satisfying \begin{align*} Ψ(X^n) = γX^{…
View article: The Tripartite Algebra of Coherence: T₇, anti-T₇ and the Monstrous Algebra as a Unified Structure
The Tripartite Algebra of Coherence: T₇, anti-T₇ and the Monstrous Algebra as a Unified Structure Open
This work introduces the Tripartite Algebra of Coherence, a unified mathematical-ontological framework composed of the T₇ algebra (positive regime), the anti-T₇ algebra (negative regime), and the Monstrous algebra (reciprocal deformation r…
View article: On (super)symmetrizing forms and Schur elements of cyclotomic Hecke-Clifford algebras
On (super)symmetrizing forms and Schur elements of cyclotomic Hecke-Clifford algebras Open
In this paper, we introduce Schur elements for supersymmetrizing superalgebras. We show that the cyclotomic Hecke-Clifford algebra $\mathcal{H}^f_{c}(n)$ is supersymmetric if $f=f^{(\mathtt{0})}_{\underline{Q}}$ and, symmetric if $f=f^{(\m…
View article: Theory of the Static-Dynamic Recursive Information Space (SDRIS) - General S-DRISS with Extended Mediator Matrix
Theory of the Static-Dynamic Recursive Information Space (SDRIS) - General S-DRISS with Extended Mediator Matrix Open
This is a concise overview of G-SDRISS (Theory of the Static–Dynamic Recursive Information Space), Axiomatic System Version C-2a1, including the extended Matrix Mediator. It outlines the conceptual path from the primal 4-dimensional origin…
View article: On (super)symmetrizing forms and Schur elements of cyclotomic Hecke-Clifford algebras
On (super)symmetrizing forms and Schur elements of cyclotomic Hecke-Clifford algebras Open
In this paper, we introduce Schur elements for supersymmetrizing superalgebras. We show that the cyclotomic Hecke-Clifford algebra $\mathcal{H}^f_{c}(n)$ is supersymmetric if $f=f^{(\mathtt{0})}_{\underline{Q}}$ and, symmetric if $f=f^{(\m…
View article: The Geometry of Near-Linear Dependence
The Geometry of Near-Linear Dependence Open
Near-linear dependence is a pervasive phenomenon in numerical linear algebra, statistics, and various scientific computing applications, posing significant challenges to the stability and accuracy of computational methods. While exact line…
View article: The Geometry of Near-Linear Dependence
The Geometry of Near-Linear Dependence Open
Near-linear dependence is a pervasive phenomenon in numerical linear algebra, statistics, and various scientific computing applications, posing significant challenges to the stability and accuracy of computational methods. While exact line…
View article: STELS ALGEBRA
STELS ALGEBRA Open
Stels numbers are multidimensional hypercomplex numbers arranged in Rubik-like hypercubes.The exponential growth of Sn and the rules of Stels algebra allow generating new sequences,matrices, and algorithms for computation and cryptography.3
View article: Explicit Formulas and Combinatorial Interpretation of Triangular Arrays
Explicit Formulas and Combinatorial Interpretation of Triangular Arrays Open
In this work, the weighted paths to interpret any triangular array of the form \[ T(n,k)=(a_2 n + a_1 k + a_0)\,T(n-1,k) + (b_2 n + b_1 k + b_0)\,T(n-1,k-1), \] allowing a structural analysis of the coefficients $\big(T(n,k)\big)_{n,k\in \…