Linear & Multilinear Algebra

Research interests of members of the Linear & Multilinear Algebra section include:

• Average sizes of kernels (Angela Carnevale, Tobias Rossmann) 

• Rank conditions in spaces of matrices (Angela Carnevale, Rachel Quinlan, Tobias Rossmann) 

• Categorical aspects of linear & multilinear algebra (Joshua Maglione, Tobias Rossmann) 
• Numerical Linear Algebra (Niall Madden) 
  
  
• Rank constrained completability of matrices and tensors (James Cruickshank)
  
  

Rank constrained completion problems arise from many application domains. Typically one has partial information about the entries of a tensor and an upper bound on the rank and the question is whether or not the missing entries can be recovered. This problem arises naturally in areas such as data science and it also has connections to classical topics in algebraic geometry such as the Alexander-Hirschowitz Theorem.   

Numerical linear algebra research in the de Brún Centre is mainly focused on the development of preconditioners for the accurate and efficient solution of large linear systems that arise in the discretization of partial differential equations. 

Cluster members: Angela Carnevale, James Cruickshank, Niall Madden, Joshua Maglione, Rachel Quinlan, Tobias Rossmann, Emil Sköldberg.