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mathematics (231) 231
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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
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
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
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
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
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
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
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
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
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
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
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
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
Journal Article
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