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## Search Articles

2005, ISBN 3764373490, xii, 357

Book

1974, Ergebnisse der Mathematik und ihrer Grenzgebiete, Volume Bd. 78, 223

Book

1986, ISBN 9783764317744, Volume 20., 200

Book

Linear algebra and its applications, ISSN 0024-3795, 11/2014, Volume 461, pp. 271 - 317

An almost Pontryagin space A is an inner product space which admits a direct and orthogonal decomposition of the form A=A>[+˙]A...

Reproducing kernel | Degenerate inner product | Indefinite inner product | Completion | Almost Pontryagin space | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Reproducing kernel | Degenerate inner product | Indefinite inner product | Completion | Almost Pontryagin space | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Journal Article

The Electronic journal of linear algebra, ISSN 1537-9582, 2012, Volume 23, pp. 1023 - 1039

The notion of quasihyponormal and strongly quasihyponormal matrices is introduced in spaces equipped with possibly degenerate indefinite inner product, based on the works that studied hyponormal...

Adjoint | H-Hyponormal | H-Quasihyponormal | Indefinite inner product | Invariant semidefinite subspaces | Linear relation | Strongly H-quasihyponormal | Physical Sciences | Mathematics | Science & Technology

Adjoint | H-Hyponormal | H-Quasihyponormal | Indefinite inner product | Invariant semidefinite subspaces | Linear relation | Strongly H-quasihyponormal | Physical Sciences | Mathematics | Science & Technology

Journal Article

Applied mathematics and computation, ISSN 0096-3003, 03/2015, Volume 254, pp. 157 - 171

We investigate full-rank representations of {2,3∼} and {2,4∼}-inverses with prescribed rank as well as with prescribed range and null space in an indefinite inner product space...

Minkowski inverse | [formula omitted]-inverse | Indefinite inner product | Moore–Penrose inverse | inverse | 2, 4 | 2, 3 | Moore-Penrose inverse | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Minkowski inverse | [formula omitted]-inverse | Indefinite inner product | Moore–Penrose inverse | inverse | 2, 4 | 2, 3 | Moore-Penrose inverse | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Journal Article

1983, Operator theory, advances and applications, ISBN 376431527X, Volume 8, xvii, 374

Book

Journal of optimization theory and applications, ISSN 0022-3239, 4/2008, Volume 137, Issue 1, pp. 99 - 104

In this paper, we study the Farkas alternative over indefinite inner product spaces using the recently proposed indefinite matrix product.

Calculus of Variations and Optimal Control; Optimization | Indefinite inner product spaces | Operations Research/Decision Theory | Farkas alternative | Mathematics | Theory of Computation | Engineering, general | Applications of Mathematics | Optimization | Indefinite matrix products | Operations Research & Management Science | Physical Sciences | Mathematics, Applied | Technology | Science & Technology | Studies | Mathematical programming | Theorems

Calculus of Variations and Optimal Control; Optimization | Indefinite inner product spaces | Operations Research/Decision Theory | Farkas alternative | Mathematics | Theory of Computation | Engineering, general | Applications of Mathematics | Optimization | Indefinite matrix products | Operations Research & Management Science | Physical Sciences | Mathematics, Applied | Technology | Science & Technology | Studies | Mathematical programming | Theorems

Journal Article

1997, Pitman monographs and surveys in pure and applied mathematics, Volume 89, 602

Book

Linear algebra and its applications, ISSN 0024-3795, 10/2017, Volume 531, pp. 356 - 374

Let A:U→V be a linear mapping between vector spaces U and V over a field or skew field F with symmetric, or skew-symmetric, or Hermitian forms B:U×U→F and C:V×V→F...

Hermitian spaces | Indefinite inner product spaces | Canonical forms | Quivers with involution | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Vector space | Quaternions | Linear algebra | Classification | Mathematical functions | Vector spaces | Symmetry | Mathematics - Representation Theory

Hermitian spaces | Indefinite inner product spaces | Canonical forms | Quivers with involution | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Vector space | Quaternions | Linear algebra | Classification | Mathematical functions | Vector spaces | Symmetry | Mathematics - Representation Theory

Journal Article

Linear algebra and its applications, ISSN 0024-3795, 02/2020, Volume 587, pp. 92 - 110

Let V be a vector space over a field F with scalar product given by a nondegenerate sesquilinear form whose matrix is diagonal in some basis. If F...

Selfadjoint operators | Indefinite inner product spaces | Isometric operators | H-unitary matrices | Unitary operators | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Operators (mathematics) | Vector space | Matrices (mathematics) | Mathematics - Representation Theory

Selfadjoint operators | Indefinite inner product spaces | Isometric operators | H-unitary matrices | Unitary operators | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Operators (mathematics) | Vector space | Matrices (mathematics) | Mathematics - Representation Theory

Journal Article

The Electronic journal of linear algebra, ISSN 1081-3810, 2006, Volume 15, pp. 50 - 83

Canonical forms are developed for several sets of matrices that are normal with respect to an indefinite inner product induced by a nonsingular Hermitian, symmetric, or skew-symmetric matrix...

Bilinear forms | Sesquilinear forms | Selfadjoint matrices | Unitary matrices | Normal matrices | Skewadjoint matrices | Indefinite inner products | Physical Sciences | Mathematics | Science & Technology

Bilinear forms | Sesquilinear forms | Selfadjoint matrices | Unitary matrices | Normal matrices | Skewadjoint matrices | Indefinite inner products | Physical Sciences | Mathematics | Science & Technology

Journal Article

Linear algebra and its applications, ISSN 0024-3795, 03/2017, Volume 516, pp. 143 - 166

... (we call the last matrix normal neutral involutory). Here the words normal, unitary, selfadjoint and neutral are understood with respect to an indefinite inner product.

Indefinite inner product | Neutral involution | Normal matrix | Sign function | Polar decomposition | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Eigenvalues | Matrix | Linear algebra | Symmetry

Indefinite inner product | Neutral involution | Normal matrix | Sign function | Polar decomposition | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology | Eigenvalues | Matrix | Linear algebra | Symmetry

Journal Article

Chinese annals of mathematics. Serie B, ISSN 0252-9599, 2005, Volume 26, Issue 4, pp. 569 - 582

Journal Article

Journal of geometry and physics, ISSN 0393-0440, 09/2010, Volume 60, Issue 9, pp. 1190 - 1208

....
In the first part of this paper we collect the common properties of the semi- and indefinite inner products and define the semi-indefinite inner product as well as the corresponding semi-indefinite inner product space...

Group of isometries | James orthogonality | Birkhoff orthogonality | Finsler space | Semi-definite inner product | Lorentz geometry | Minkowski space | Normed linear space | Indefinite inner product | Finite-dimensional real Banach space | Physical Sciences | Mathematics | Physics | Physics, Mathematical | Science & Technology | Mathematics - Metric Geometry

Group of isometries | James orthogonality | Birkhoff orthogonality | Finsler space | Semi-definite inner product | Lorentz geometry | Minkowski space | Normed linear space | Indefinite inner product | Finite-dimensional real Banach space | Physical Sciences | Mathematics | Physics | Physics, Mathematical | Science & Technology | Mathematics - Metric Geometry

Journal Article

Filomat, ISSN 0354-5180, 2017, Volume 31, Issue 12, pp. 3847 - 3857

We present the definition and some properties for the Moore-Penrose inverse in possibly degenerate indefinite inner product spaces...

Indefinite inner product | Linear relation | Adjoint | Moore-Penrose inverse | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Indefinite inner product | Linear relation | Adjoint | Moore-Penrose inverse | Physical Sciences | Mathematics | Mathematics, Applied | Science & Technology

Journal Article

The Electronic journal of linear algebra, ISSN 1081-3810, 02/2006, Volume 15, pp. 84 - 106

Polynomially normal matrices in real indefinite inner product spaces are studied, i.e...

Selfadjoint matrices | Unitary matrices | Normal matrices | Skewadjoint matrices | Essential decomposition | Indefinite inner products | Physical Sciences | Mathematics | Science & Technology

Selfadjoint matrices | Unitary matrices | Normal matrices | Skewadjoint matrices | Essential decomposition | Indefinite inner products | Physical Sciences | Mathematics | Science & Technology

Journal Article

Journal of functional analysis, ISSN 0022-1236, 2011, Volume 260, Issue 4, pp. 1045 - 1059

We study S-spaces and operators therein. An S-space is a Hilbert space
(
S
,
(
⋅
,
−
)
)
with an additional inner product given by
[
⋅
,
−
]
:
=
(
U...

Krein space | Selfadjoint operators | Invariant subspaces | S-space | Indefinite inner products | Physical Sciences | Mathematics | Science & Technology

Krein space | Selfadjoint operators | Invariant subspaces | S-space | Indefinite inner products | Physical Sciences | Mathematics | Science & Technology

Journal Article

Operators and Matrices, ISSN 1846-3886, 09/2015, Volume 9, Issue 3, pp. 481 - 506

Journal Article

Indagationes mathematicae, ISSN 0019-3577, 01/2016, Volume 27, Issue 1, pp. 11 - 19

.... Also, we prove some reverse inequalities for indefinite inner product space. Moreover, we establish some refinements for the reverse of Schwarz inequality as well.

Reverse Schwarz inequality | Indefinite inner product | Minkowski inner product | Reverse Heinz–Kato–Furuta inequality | Reverse Heinz-Kato-Furuta inequality | Physical Sciences | Mathematics | Science & Technology

Reverse Schwarz inequality | Indefinite inner product | Minkowski inner product | Reverse Heinz–Kato–Furuta inequality | Reverse Heinz-Kato-Furuta inequality | Physical Sciences | Mathematics | Science & Technology

Journal Article

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