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All about the ⊥ with its applications in the linear statistical models

100%

Markiewicz A., Puntanen S.

Open Mathematics

2015

tom 13

nr 1

For an n x m real matrix A the matrix A⊥ is defined as a matrix spanning the orthocomplement of the column space of A, when the orthogonality is defined with respect to the standard inner product ⟨x, y⟩ = x'y. In this paper we collect together various properties of the ⊥ operation and its applications in linear statistical models. Results covering the more general inner products are also considered. We also provide a rather extensive list of references

On orderings induced by the Loewner partial ordering

100%

Hauke J., Markiewicz A.

Applicationes Mathematicae

1993-1995

tom 22

nr 2

145-154

The partial ordering induced by the Loewner partial ordering on the convex cone comprising all matrices which multiplied by a given positive definite matrix become nonnegative definite is considered. Its relation to orderings which are induced by the Loewner partial ordering of the squares of matrices is presented. Some extensions of the latter orderings and their comparison to star orderings are given.

Ograniczanie wyników

1 Applicationes Mathematicae

1 Open Mathematics

2 Markiewicz A.

1 Hauke J.

1 Puntanen S.

1 2015

1 1994

Wyniki wyszukiwania

All about the ⊥ with its applications in the linear statistical models

On orderings induced by the Loewner partial ordering