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If H1 is an n × n and H2 an m × m invertible Hermitian matrix and X and Y are arbitrary complex m × n matrices, we call the last matrices equivalent if X = U2YU1 for some H1-unitary matrix U1 and… (More)

In our previous paper [2] a special class of normal operators acting in spaces with indefinite scalar product was introduced. The operators from this class are characterized by the property that in… (More)

A special class of normal operators acting in spaces with indefinite scalar products is studied. The operators from this class are characterized by the property that, in a natural basis, their… (More)

Abstract Several classes of polar decompositions of real and complex matrices with respect to a given indefinite scalar product are studied. Matrices that admit such polar decompositions are… (More)

- Boris Reichstein
- 1987

Abstract Sufficient conditions for a cubic form ω in n variables to be representable as a sum of cubes of n + m [ m ⩽(n−2) 2 ] linear forms are derived. For m =0, 1 the conditions are also necessary… (More)

Witt's theorem on the extension of H-isometries to H-unitary matrices with respect to the scalar product generated by a self-adjoint nonsingular matrix H is studied in detail. All possible extensions… (More)

Polar decompositions X = UA of real and complex matrices X with respect to the scalar product generated by a given indefinite nonsingular matrix H are studied in the following special cases: (1) X is… (More)

- Boris Reichstein
- 1986

Abstract The concept of a symmetric operator relative to a quadratic form is extended to a k -form ϕ acting in n -space L n for any k ⩾2. It is shown how to embed L 2 into L r with the smallest… (More)

- Boris Reichstein
- 1989

The problem of the classification of invariant subspaces of a linear operator is shown to be at least as complex as the problem of the classification of arbitrary pairs of square matrices up to… (More)