Stephen J. Kirkland is a Stokes Professor at the National University of Ireland, Maynooth. He is editor-in-chief of Linear and Multilinear Algebra and serves on the editorial boards of several other journals. Dr. Kirkland’s research interests are primarily in matrix theory and graph theory, with an emphasis on the interconnections between these two areas.Michael Neumann was the Stuart and Joan Sidney Professor of Mathematics and a Board of Trustees Distinguished Professor at the University of Connecticut. Dr. Neumann published more than 160 mathematical papers, mainly in matrix theory, numerical linear algebra, and numerical analysis.

• Motivation and Examples. The Group Inverse. Group Inverses and Derivatives of Matrix Functions. Perron Eigenpair in Demographic Applications. The Group Inverse in Markov Chains. Mean First Passage Times for Markov Chains. Applications of the Group Inverse to Laplacian Matrices. Computing the Group Inverse. Bibliography.

Stephen J. Kirkland is a Stokes Professor at the National University of Ireland, Maynooth. He is editor-in-chief of Linear and Multilinear Algebra and serves on the editorial boards of several other journals. Dr. Kirkland’s research interests are primarily in matrix theory and graph theory, with an emphasis on the interconnections between these two areas.Michael Neumann was the Stuart and Joan Sidney Professor of Mathematics and a Board of Trustees Distinguished Professor at the University of Connecticut. Dr. Neumann published more than 160 mathematical papers, mainly in matrix theory, numerical linear algebra, and numerical analysis.

• Motivation and Examples. The Group Inverse. Group Inverses and Derivatives of Matrix Functions. Perron Eigenpair in Demographic Applications. The Group Inverse in Markov Chains. Mean First Passage Times for Markov Chains. Applications of the Group Inverse to Laplacian Matrices. Computing the Group Inverse. Bibliography.