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We consider problems in invariant theory related to the classification of four vector subspaces of an $n$ -dimensional complex vector space. We use castling techniques to quickly recover results of Howe and Huang on invariants. We further obtain information about principal isotropy groups, equidimensionality and the modules of covariants.

Invariants of orthogonal $G$ -modules from the character table.

Nebe, Gabriele (2000)

Experimental Mathematics

Inverse eigenvalue problem of cell matrices

Sreyaun Khim, Kijti Rodtes (2019)

Czechoslovak Mathematical Journal

We consider the problem of reconstructing an $n \times n$ cell matrix $D (\vec{x})$ constructed from a vector $\vec{x} = (x_{1}, x_{2}, \dots, x_{n})$ of positive real numbers, from a given set of spectral data. In addition, we show that the spectra of cell matrices $D (\vec{x})$ and $D (π (\vec{x}))$ are the same for every permutation $π \in S_{n}$ .

Inverse eigenvalue problem of unitary Hessenberg matrices.

Wu, Chunhong, Lu, Linzhang (2009)

Discrete Dynamics in Nature and Society

Inverse interval matrix: a survey.

Rohn, Jiri, Farhadsefat, Raena (2011)

ELA. The Electronic Journal of Linear Algebra [electronic only]

Inverse series relations, formal power series and Blodgett-Gessel's type binomial identities.

Chu, Wenchang (1992)

Séminaire Lotharingien de Combinatoire [electronic only]

Inverse series relations, formal power series and Blodgett-Gessel's type binomial identities.

Chu Wenchang (1997)

Collectanea Mathematica

A pair of simple bivariate inverse series relations are used by embedding machinery to produce several double summation formulae on shifted factorials (or binomial coefficients), including the evaluation due to Blodgett-Gessel. Their q-analogues are established in the second section. Some generalized convolutions are presented through formal power series manipulation.

Inverse spectral problems for tridiagonal $N$ by $N$ complex Hamiltonians.

Guseinov, Gusein Sh. (2009)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Inversion des matrices de Toeplitz dont le symbole admet un zéro d’ordre rationnel positif, valeur propre minimale

Philippe Rambour, Abdellatif Seghier (2012)

Annales de la faculté des sciences de Toulouse Mathématiques

Cet article présente trois résultats distincts. Dans une première partie nous donnons l’asymptotique quand $N$ tend vers l’infini des coefficients des polynômes orthogonaux de degré $N$ associés au poids $ϕ_{α} (θ) = {| 1 - e^{i θ} |}^{2 α} f_{1} (e^{i θ})$ , où $f_{1}$ est une fonction strictement positive suffisamment régulière et $α > \frac{1}{2}, α \in ℝ ∖ ℕ$ . Nous en déduisons l’asymptotique des éléments de l’inverse de la matrice de Toeplitz $T_{N} (ϕ_{α})$ au moyen d’un noyau intégral $G_{α} .$ Nous prolongeons ensuite un résultat de A. Böttcher et H. Windom relatif à l’asymptotique de la valeur propre...

Inversion d’un opérateur de Toeplitz tronqué à symbole matriciel et théorèmes-limite de Szegö

Jean Chanzy (2006)

Annales mathématiques Blaise Pascal

Ce travail est une étude théorique d’opérateurs de Toeplitz dont le symbole est une fonction matricielle régulière définie positive partout sur le tore à une dimension. Nous proposons d’abord une formule d’inversion exacte pour un opérateur de Toeplitz à symbole matriciel, démontrée au moyen d’un théorème établi en annexe et donnant la solution du problème de la prédiction relatif à un passé fini pour un processus stationnaire du second ordre. Nous établissons ensuite, à partir de cet inverse, un...

Inversion of $3 \times 3$ partitioned matrices in investigation of the twoepoch linear model with the nuisance parameters

Karel Hron (2006)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The estimation procedures in the multiepoch (and specially twoepoch) linear regression models with the nuisance parameters that were described in [2], Chapter 9, frequently need finding the inverse of a $3 \times 3$ partitioned matrix. We use different kinds of such inversion in dependence on simplicity of the result, similarly as in well known Rohde formula for $2 \times 2$ partitioned matrix. We will show some of these formulas, also methods how to get the other formulas, and then we applicate the formulas in estimation...

Inversion of bilateral basic hypergeometric series.

Schlosser, Michael (2003)

The Electronic Journal of Combinatorics [electronic only]

Inversion of incidence mappings.

Krämer, Helmut (1997)

Séminaire Lotharingien de Combinatoire [electronic only]

Inversion of square matrices in processors with limited calculation abillities

Krzysztof Janiszowski (2003)

International Journal of Applied Mathematics and Computer Science

An iterative inversion algorithm for a class of square matrices is derived and tested. The inverted matrix can be defined over both real and complex fields. This algorithm is based only on the operations of addition and multiplication. The numerics of the algorithm can cope with a short number representation and therefore can be very useful in the case of processors with limited possibilities, like different neuro-computers and accelerator cards. The quality of inversion can be traced and tested....

Inversion of Tridiagonal Matrices.

J.W. Lewis (1982)

Numerische Mathematik

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