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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

Equalities for orthogonal projectors and their operations

84%

Tian Y.

Open Mathematics

2010

tom 8

nr 5

855-870

A complex square matrix A is called an orthogonal projector if A 2 = A = A*, where A* denotes the conjugate transpose of A. In this paper, we give a comprehensive investigation to matrix expressions consisting of orthogonal projectors and their properties through ranks of matrices. We first collect some well-known rank formulas for orthogonal projectors and their operations, and then establish various new rank formulas for matrix expressions composed by orthogonal projectors. As applications, we derive necessary and sufficient conditions for various equalities for orthogonal projectors and their operations to hold.

Ograniczanie wyników

2 Open Mathematics

1 Markiewicz A.

1 Puntanen S.

1 Tian Y.

1 2015

1 2010

Wyniki wyszukiwania

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

Equalities for orthogonal projectors and their operations