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This expository paper focuses on the study of extreme surjective functions in ℝℝ. We present several different types of extreme surjectivity by providing examples and crucial properties. These examples help us to establish a hierarchy within the different classes of surjectivity we deal with. The classes presented here are: everywhere surjective functions, strongly everywhere surjective functions, κ-everywhere surjective functions, perfectly everywhere surjective functions and Jones functions. The...

A new characterization of generalized complementary basic matrices

Miroslav Fiedler, Frank J. Hall (2014)

Special Matrices

In this paper, a new characterization of previously studied generalized complementary basic matrices is obtained. It is in terms of ranks and structure ranks of submatrices defined by certain diagonal positions. The results concern both the irreducible and general cases.

A New Characterization of Generalized Complementary Basic Matrices

Miroslav Fiedler, Frank J. Hall (2014)

Special Matrices

A new equivalent condition of the reverse order law for $G$ -inverses of multiple matrix products.

Zheng, Bing, Xiong, Zhiping (2008)

ELA. The Electronic Journal of Linear Algebra [electronic only]

A new rank formula for idempotent matrices with applications

Yong Ge Tian, George P. H. Styan (2002)

Commentationes Mathematicae Universitatis Carolinae

It is shown that $rank (P^{*} A Q) = rank (P^{*} A) + rank (A Q) - rank (A),$ where $A$ is idempotent, $[P, Q]$ has full row rank and $P^{*} Q = 0$ . Some applications of the rank formula to generalized inverses of matrices are also presented.

A new simple approach to linear dependence

Ladislav Beran (2004)

Acta Universitatis Carolinae. Mathematica et Physica

A new solvable condition for a pair of generalized Sylvester equations.

Wang, Qing-Wen, Zhang, Hua-Sheng, Song, Guang-Jing (2009)

ELA. The Electronic Journal of Linear Algebra [electronic only]

A note on hypervector spaces

Sanjay Roy, Tapas K. Samanta (2011)

Discussiones Mathematicae - General Algebra and Applications

The main aim of this paper is to generalize the concept of vector space by the hyperstructure. We generalize some definitions such as hypersubspaces, linear combination, Hamel basis, linearly dependence and linearly independence. A few important results like deletion theorem, extension theorem, dimension theorem have been established in this hypervector space.

A note on minimum rank and maximum nullity of sign patterns.

Hogben, Leslie (2011)

ELA. The Electronic Journal of Linear Algebra [electronic only]

A note on preserving the spark of a matrix

Marcin Skrzyński (2015)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

Let Mm×n(F) be the vector space of all m×n matrices over a field F. In the case where m ≥ n, char(F) ≠ 2 and F has at least five elements, we give a complete characterization of linear maps Φ: Mm×n(F) → Mm×n(F) such that spark(Φ(A)) = spark(A) for any A ∈Mm×n(F).

A note on the continuity of projection matrices with application to the asymptotic distribution of quadratic forms

G. Forchini (2005)

Applicationes Mathematicae

This paper investigates the continuity of projection matrices and illustrates an important application of this property to the derivation of the asymptotic distribution of quadratic forms. We give a new proof and an extension of a result of Stewart (1977).

A note on the cp-rank of matrices generated by Soules matrices.

Shaked-Monderer, Naomi (2005)

ELA. The Electronic Journal of Linear Algebra [electronic only]

A note on the ranks of set-inclusion matrices.

de Caen, D. (2001)

The Electronic Journal of Combinatorics [electronic only]

A remark on spaces over a special local ring

Marek Jukl (1998)

Mathematica Bohemica

This paper deals with A-spaces in the sense of McDonald over linear algebras A of a certain type. Necessary and sufficient conditions for a submodule to be an A-space are derived.

A transvection decomposition in GL(n,2)

Clorinda De Vivo, Claudia Metelli (2002)

Colloquium Mathematicae

An algorithm is given to decompose an automorphism of a finite vector space over ℤ₂ into a product of transvections. The procedure uses partitions of the indexing set of a redundant base. With respect to tents, i.e. finite ℤ₂-representations generated by a redundant base, this is a decomposition into base changes.

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