Primitive spaces of matrices of bounded rank

M. D. Atkinson, Seth Lloyd

Type: Article

Publication Date: 1981-04-01

Citations: 18

DOI: https://doi.org/10.1017/s144678870001795x

Abstract

Abstract A weak canonical form is derived for vector spaces of m × n matrices all of rank at most r . This shows that the structure of such spaces is controlled by the structure of an associated ‘primitive’ space. In the case of primitive spaces it is shown that m and n are bounded by functions of r and that these bounds are tight.

Locations

Journal of the Australian Mathematical Society - View - PDF

Similar Works

Action	Title	Year	Authors
+ PDF Chat	Primitive spaces of matrices of bounded rank. II	1983	M. D. Atkinson
+ PDF Chat	FROM PRIMITIVE SPACES OF BOUNDED RANK MATRICES TO A GENERALIZED GERSTENHABER THEOREM	2013	Clément de Seguins Pazzis
+	Normal forms in matrix spaces	2000	Genrich Belitskii
+	Some insights into rank conditions of vector subspaces	2024	Zoran Z. Petrović Zoran S. Pucanović Marko Pešović Miloš Kovačević
+	Matrix Spaces	2007
+	Matrix Spaces	2007
+	Normal forms of matrices	1994	P. M. Cohn
+	Normal forms of matrices	2017	P. M. Cohn
+	Spaces of constant rank matrices over .	2010	Nigel Boston
+	R-matrices and symmetric spaces	1990	Jean Avan J.-M. Maillard Michel Talon
+	On affine spaces of rectangular matrices with constant rank	2024	Clément de Seguins Pazzis
+	Matrices and vector spaces	2012	K. F. Riley M. P. Hobson
+	Matrices and vector spaces	2012	K. F. Riley M. P. Hobson
+	Bases of spaces of matrices satisfying rank conditions	2008	Zoran Z. Petrović
+	A note on the rank of matrices	2014	Liqun Tao
+	Affine spaces of symmetric or alternating matrices with bounded rank	2016	Clément de Seguins Pazzis
+	The Smith normal form and reduction of weakly linear matrices	2023	Jinwang Liu Dongmei Li Tao Wu
+	A matrix version of Bloch spaces	2014
+	P-Matrices	2020	Charles R. Johnson Ronald L. Smith Michael J. Tsatsomeros
+	Algebra and Matrix Normed Spaces	2001	Seth M. Hain

Works That Cite This (19)

Action	Title	Year	Authors
+ PDF Chat	Geometric rank and linear determinantal varieties	2023	Runshi Geng
+	Primitive spaces of matrices with upper rank two over the field with two elements	2015	Clément de Seguins Pazzis
+ PDF Chat	Large affine spaces of non-singular matrices	2012	Clément de Seguins Pazzis
+	On rank-critical matrix spaces	2017	Yinan Li Youming Qiao
+	Matrix spaces with bounded number of eigenvalues	1996	Matjaž Omladič Peter Šemrl
+	Linear rank and corank preserving maps on B(H) and an application to ∗-semigroup isomorphisms of operator ideals	1998	Máté Győry Lajos Molnár Peter Šemrl
+	Large spaces of bounded rank matrices revisited	2016	Clément de Seguins Pazzis
+	Range-compatible homomorphisms on matrix spaces	2015	Clément de Seguins Pazzis
+ PDF Chat	Primitive spaces of matrices of bounded rank. II	1983	M. D. Atkinson
+ PDF Chat	Concise tensors of minimal border rank	2023	Joachim Jelisiejew J. M. Landsberg Arpan Pal

Works Cited by This (2)

Action	Title	Year	Authors
+	SPACES OF MATRICES OF BOUNDED RANK	1978	M. D. Atkinson N. M. Stephens
+	LARGE SPACES OF MATRICES OF BOUNDED RANK	1980	M. D. Atkinson Seth Lloyd