Unitary equivalence in an indefinite scalar product: An analogue of singular-value decomposition

DOI10.1016/0024-3795(93)00295-BzbMath0828.15009WikidataQ117378937 ScholiaQ117378937MaRDI QIDQ1894474

Yuri Bolshakov, Boris Raykhshteyn

Publication date: 6 September 1995

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

zbMATH Keywords

Jordan formHermitian matrixsingular-value decompositionpolar decompositioncanonical formunitary equivalenceconsistent operatorindefinite scalar product

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Quadratic and bilinear forms, inner products (15A63) Canonical forms, reductions, classification (15A21)

Related Items (19)

Finite-Dimensional Indefinite Inner Product Spaces and Applications in Numerical Analysis ⋮ Polar decompositions in finite dimensional indefinite scalar product spaces: General theory ⋮ Skew \(\phi\) polar decompositions ⋮ Classification of linear mappings between indefinite inner product spaces ⋮ The pair of operators \(T^{[*}T\) and \(TT^{[*]}\): \(J\)-dilations and canonical forms] ⋮ Classes of plus matrices in finite dimensional indefinite scalar product spaces ⋮ Stable and Efficient Computation of Generalized Polar Decompositions ⋮ Hyperbolic Pseudoinverses for Kinematics in the Euclidean Group ⋮ Polar decompositions of quaternion matrices in indefinite inner product spaces ⋮ Stability of self-adjoint square roots and polar decompositions in indefinite scalar product spaces ⋮ Normal matrices and polar decompositions indefinite inner products ⋮ Research problem: indefinite inner product normal matrices ⋮ Positive maps of second-order cones ⋮ Classes of normal matrices in indefinite inner products ⋮ A new polar decomposition in a scalar product space ⋮ Factorizations into normal matrices in indefinite inner product spaces ⋮ Singular-value-like decomposition for complex matrix triples ⋮ Singular numbers of contractions in spaces with an indefinite metric and Yamamoto's theorem ⋮ Polar decompositions and related classes of operators in spaces \(\Pi_\kappa\).

Cites Work

• Matrices and indefinite scalar products
• Matrix Analysis
• On h-unitary and block-toeplitz h-normal operators
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