Constructing invariant subspaces as kernels of commuting matrices
dc.contributor.author | Cowen, Carl C. | |
dc.contributor.author | Johnston, William | |
dc.contributor.author | Wahl, Rebecca G. | |
dc.contributor.department | Mathematical Sciences, School of Science | en_US |
dc.date.accessioned | 2020-01-31T15:26:02Z | |
dc.date.available | 2020-01-31T15:26:02Z | |
dc.date.issued | 2019-12 | |
dc.description.abstract | Given an n n matrix A over C and an invariant subspace N, a straightforward formula constructs an n n matrix N that commutes with A and has N = kerN. For Q a matrix putting A into Jordan canonical form, J = Q1AQ, we get N = Q1M where M= ker(M) is an invariant subspace for J with M commuting with J. In the formula J = PZT1Pt, the matrices Z and T are m m and P is an n m row selection matrix. If N is a marked subspace, m = n and Z is an n n block diagonal matrix, and if N is not a marked subspace, then m > n and Z is an m m near-diagonal block matrix. Strikingly, each block of Z is a monomial of a nite-dimensional backward shift. Each possible form of Z is easily arranged in a lattice structure isomorphic to and thereby displaying the complete invariant subspace lattice L(A) for A. | en_US |
dc.eprint.version | Author's manuscript | en_US |
dc.identifier.citation | Cowen, C. C., Johnston, W., & Wahl, R. G. (2019). Constructing invariant subspaces as kernels of commuting matrices. Linear Algebra and Its Applications, 583, 46–62. https://doi.org/10.1016/j.laa.2019.08.014 | en_US |
dc.identifier.uri | https://hdl.handle.net/1805/21943 | |
dc.language.iso | en | en_US |
dc.publisher | Elsevier | en_US |
dc.relation.isversionof | 10.1016/j.laa.2019.08.014 | en_US |
dc.relation.journal | Linear Algebra and Its Applications | en_US |
dc.rights | IUPUI Open Access Policy | en_US |
dc.source | Author | en_US |
dc.subject | invariant subspace | en_US |
dc.subject | kernel | en_US |
dc.subject | commuting matrices | en_US |
dc.title | Constructing invariant subspaces as kernels of commuting matrices | en_US |
dc.type | Article | en_US |