Steve Kirkland, Hamilton Institute, National University of Ireland Maynooth

Steve Kirkland

Stokes Professor
Hamilton Institute
National University of Ireland Maynooth

E-mail: stephen DOT kirkland AT nuim DOT ie
Phone: +353 (0)1 708 6797


Research Interests

  • Theory and applications of nonnegative matrices
  • Combinatorial matrix theory
  • Spectral graph theory

  • Professional Activities

  • Editor in Chief, Linear and Multilinear Algebra
  • Associate Editor, Linear Algebra and its Applications
  • Advisory Editor, Electronic Journal of Linear Algebra
  • Editorial Board Member, SIAM Review
  • President, International Linear Algebra Society

  • Current Graduate Students

  • Arieh Schlote , Ph.D. student, NUI Maynooth.
  • Jane Breen , Masters student, NUI Maynooth.
  • Completed Graduate Students

  • Suquin Ao, Ph.D. 1998, University of Regina. Thesis: Aspects of Chromatic Numbers and Rankings in Tournaments.
  • Ryan Tifenbach, M.Sc. 2008, University of Regina. Thesis: Strongly Self-Dual Graphs.
  • Mahmud Akelbek, Ph.D. 2008, University of Regina. Thesis: A Joint Neighbour Bound for Primitive Digraphs.
  • Michael Cavers , Ph.D. 2010, University of Regina. Thesis: The Normalized Laplacian Matrix and General Randic Index of Graphs.
  • Ryan Tifenbach , Ph.D. 2011, National University of Ireland Maynooth. Thesis: A Combinatorial Approach to Nearly Uncoupled Markov Chains.

    Postdoctoral Fellows

  • Mark Krupnik, supervised at the University of Regina, 1994-1995.
  • Sukanta Pati , supervised at the University of Regina, 1999-2001.
  • Francesco Barioli, supervised at the University of Regina, 2001-2003.
  • Sasmita Barik, supervised at the University of Regina, 2008.
  • Adam Hackett , IRCSET Postdoctoral Fellow, supervised at NUI Maynooth, 2011-2013.
  • Felix Goldberg, supervised at NUI Maynooth, 2012-present.

  • Conferences of Interest

  • POSTA 2012 , Maynooth, Ireland, 2-4 September, 2012.
  • 18th Conference of the International Linear Algebra Society , Providence, USA, 3-7 June, 2013.
  • 4th International Conference on Matrix Analysis and Applications , Konya, Turkey, 2-5 July, 2013.
  • Mat Triad, Herceg-Novi, Montenegro, 16-20 September, 2013.

  • Books

  • S. Kirkland and M. Neumann, Group Inverses of M-Matrices and their Applications, CRC Press, 2012.
  • Lectures on Matrix and Graph Methods, R. Bapat, S. Kirkland, K. Prasad and S. Puntanen, Eds, Manipal University Press, 2012.


    Journal Articles

  • C. Godsil, S. Kirkland, S. Severini and J. Smith, Number-theoretic Nature of Communication in Quantum Spin Systems, Physical Review Letters 109 (2012), 050502, 4 pages.
  • L. de Alba, J. Grout, I-J. Kim, S. Kirkland, J. McDonald and A. Yielding, Minimum Rank of Powers of Trees, Electronic Journal of Linear Algebra 23 (2012), 151-163.
  • M. Cavers, S. Cioaba, S. Fallat, D. Gregory, W. Haemers, S. Kirkland, J. McDonald and M. Tsatsomeros, Skew Adjacency Matrices of Graphs, Linear Algebra and its Applications 436 (2012), 4512-4529.
  • E. Crisostomi, A. Schlote, S. Kirkland and R. Shorten, Traffic Modelling Framework for Electric Vehicles, International Journal of Control 85 (2012), 880-897.
  • A. Zappavigna, P. Colaneri, S. Kirkland and R. Shorten, Essentially Negative News About Positive Systems, Linear Algebra and its Applications 436 (2012), 3425-3442.
  • S. Kirkland, Sign Patterns for Eigenmatrices of Nonnegative Matrices, Linear and Multilinear Algebra 59 (2011), 999-1018.
  • S. Kirkland, C. Oliveira and C. Justel, On Algebraic Connectivity Augmentation, Linear Algebra and its Applications 435 (2011), 2347-2356.
  • E. Crisostomi, S. Kirkland and R. Shorten, A Google-like Model of Road Network Dynamics and its Application to Regulation and Control, International Journal of Control 84 (2011), 633-651.
  • S. Barik, S. Fallat and S. Kirkland, On Hadamard Diagonalizable Graphs, Linear Algebra and its Applications 435 (2011), 1885-1902.
  • S. Kirkland and D. Paul, Bipartite Subgraphs and the Signless Laplacian Matrix, Applicable Analysis and Discrete Mathematics 5 (2011), 1-13.
  • S. Kirkland and S. Severini, Spin Systems Dynamics and Fault Detection in Threshold Networks, Physical Review A 83 (2011), 012310, 5 pages.
  • S. Kirkland, Fastest Expected Time to Mixing for a Markov Chain on a Directed Graph, Linear Algebra and its Applications 433 (2010), 1988-1996.
  • S. Kirkland, Column Sums and the Conditioning of the Stationary Distribution for a Stochastic Matrix, Operators and Matrices 4 (2010), 431-443.
  • M. Catral, S. Kirkland, M. Neumann and N-S Sze, The Kemeny Constant for Finite Homogeneous Ergodic Markov Chains, Journal of Scientific Computing 45 (2010), 151-166.
  • M. Cavers, S. Fallat and S. Kirkland, On the Normalized Laplacian Energy and General Randic Index R_{-1} of Graphs, Linear Algebra and its Applications 433 (2010), 172-190.
  • S. Kirkland, M. de Freitas, R. Del Vecchio and N. Abreu, Split Nonthreshold Laplacian Integral Graphs, Linear and Multilinear Algebra 58 (2010), 221-233.
  • C. Oliveira, L. Lima, N. Abreu and S. Kirkland, Bounds on the Q-Spectrum of a Graph , Linear Algebra and its Applications 432 (2010), 2342-2351.
  • R. Brualdi and S. Kirkland, Totally Nonnegative (0,1)-Matrices , Linear Algebra and its Applications 432 (2010), 1650-1662.
  • S. Kirkland, Algebraic Connectivity for Vertex-Deleted Subgraphs, and a Notion of Vertex Centrality , Discrete Mathematics 310 (2010), 911-921.
  • S. Kirkland, Subdominant Eigenvalues for Stochastic Matrices with Given Column Sums, Electronic Journal of Linear Algebra 18 (2009), 784-800.
  • S. Kirkland and M. Neumann, The Case of Equality in the Dobrushin-Deutsch-Zenger Bound , Linear Algebra and its Applications 431 (2009), 2373-2394.
  • R. Tifenbach and S. Kirkland, Directed Intervals and the Dual of a Graph , Linear Algebra and its Applications 431 (2009), 792-807.
  • S. Kirkland, Near Threshold Graphs , Electronic Journal of Combinatorics 16 (2009), Research Paper 42, 20 pages.
  • S. Kirkland, A Cycle-based Bound for Subdominant Eigenvalues of Stochastic Matrices , Linear and Multilinear Algebra 57 (2009),247-266.
  • M. Akelbek and S. Kirkland, Primitive Digraphs with Largest Scrambling Index , Linear Algebra and its Applications 430 (2009), 1111-1130.
  • M. Akelbek and S. Kirkland, Coefficients of Ergodicity and the Scrambling Index , Linear Algebra and its Applications 430 (2009), 1099-1110.
  • S. Kirkland, M. Neumann and N-S Sze, On Optimal Condition Numbers For Markov Chains, Numerische Mathematik 110 (2008), 521-537.
  • S. Kirkland, Laplacian Integral Graphs with Maximum Degree 3, the Electronic Journal of Combinatorics 15 (2008), Research Paper 120, 42 pages.
  • S. Kirkland, A Note on a Distance Bound Using Eigenvalues of the Normalized Laplacian Matrix, Electronic Journal of Linear Algebra 16 (2007), 204-207.
  • S. Kirkland, M. Neumann and J. Xu, Transition Matrices for Well-conditioned Markov Chains, Linear Algebra and its Applications 424 (2007), 118-131.
  • S. Kirkland, Constructably Laplacian Integral Graphs, Linear Algebra and its Applications 423 (2007), 3-21.
  • S. Akbari and S. Kirkland, On Unimodular Graphs, Linear Algebra and its Applications 421 (2007), 3-15.
  • S. Kirkland, Limit Points for Normalized Laplacian Eigenvalues, Electronic Journal of Linear Algebra 15 (2006), 337-344.
  • S. Kirkland, Conditioning of the Entries in the Stationary Vector of a Google-type Matrix, Linear Algebra and its Applications 418 (2006), 665-681.
  • S. Kirkland, C.-K. Li and S. Schreiber, On the Evolution of Dispersal in Patchy Landscapes, SIAM Journal on Applied Mathematics 66 (2006), 1366-1382.
  • I. Ipsen and S. Kirkland, Convergence Analysis of a Pagerank Updating Algorithm by Langville and Meyer, SIAM Journal on Matrix Analysis and Applications 27 (2006), 952-967.
  • R. Brualdi and S. Kirkland, Aztec Diamonds and Digraphs, and Hankel Determinants of Schroder Numbers, Journal of Combinatorial Theory B 94 (2005), 334-351.
  • S. Fallat, S. Kirkland, J. Molitierno and M. Neumann, On Graphs Whose Laplacian Matrices Have Distinct Integer Eigenvalues, Journal of Graph Theory 50 (2005), 162-174.
  • S. Kirkland, Completion of Laplacian Integral Graphs via Edge Addition, Discrete Mathematics 295 (2005), 75-90.
  • R. Bapat, S. Kirkland and M. Neumann, On Distance Matrices and Laplacians, Linear Algebra and its Applications 401 (2005), 193-209.
  • S. Kirkland, Sensitivity Of The Stable Distribution Vector for a Size-Classified Population Model, Linear Algebra and its Applications 398 (2005), 3-23.
  • S. Kirkland, Girth and Subdominant Eigenvalues for Stochastic Matrices, Electronic Journal of Linear Algebra 12 (2004/2005), 25-41.
  • S. Kirkland, M. Neumann and J. Xu, Convexity and Elasticity of the Growth Rate in Stage-Based Population Models, SIAM Journal on Matrix Analysis and Applications 26 (2004), 170-185.
  • S. Kirkland, A Combinatorial Approach to the Conditioning of a Single Entry in the Stationary Distribution for a Markov Chain, Electronic Journal of Linear Algebra 11 (2004), 168-179.
  • S. Kirkland, Digraph-Based Conditioning for Markov Chains, Linear Algebra and its Applications 385 (2004), 81-93.
  • S. Kirkland, A Characterization of Spectral Integral Variation in Two Places for Laplacian Matrices, Linear and Multilinear Algebra 52 (2004), 79-98.
  • S. Kirkland and M. Neumann, On Algebraic Connectivity as a Function of an Edge Weight, Linear and Multilinear Algebra 52 (2004), 17-33.
  • L. Beasley and S. Kirkland, A Note on k-Primitive Directed Graphs, Linear Algebra and its Applications 373 (2003), 67-74.
  • S. Fallat, S. Kirkland and S. Pati, On Graphs with Algebraic Connectivity Equal to Minimum Edge Density, Linear Algebra and its Applications 373 (2003), 31-50.
  • S. Kirkland, A Note on Limit Points for Algebraic Connectivity, Linear Algebra and its Applications 373 (2003), 5-11.
  • S. Fallat, S. Kirkland and S. Pati, Maximizing Algebraic Connectivity over Unicyclic Graphs, with Linear and Multilinear Algebra 51 (2003), 221-241.
  • R. Hemasinha, S. Kirkland, J. Stuart and J. Weaver, Properties of the Brualdi-Li Tournament Matrix, Linear Algebra and its Applications 361 (2003), 63-73.
  • S. Kirkland, An Upper Bound on the Perron Value of an Almost Regular Tournament Matrix, Linear Algebra and its Applications 361 (2003), 7-22.
  • S. Kirkland, Conditioning Properties of the Stationary Vector for a Markov Chain, Electronic Journal of Linear Algebra 10 (2003), 1-15.
  • S. Kirkland, M. Neumann, N. Ormes and J. Xu, On the Elasticity of the Perron Root of a Nonnegative Matrix, SIAM Journal on Matrix Analysis and Applications 24 (2002), 454-464.
  • S. Kirkland and S. Pati, On Absolute Algebraic Connectivity and Vertex Connectivity for Graphs, Linear and Multilinear Algebra 50 (2002), 253-284.
  • S. Fallat, S. Kirkland and S. Pati, Minimizing Algebraic Connectivity Over Connected Graphs with Fixed Girth, Discrete Mathematics 254 (2002), 115-142.
  • S. Kirkland, On a Question Concerning Condition Numbers for Markov Chains, SIAM Journal on Matrix Analysis and Applications 23 (2002), 1109-1119.
  • S. Kirkland, J. Molitierno, M. Neumann and B. Shader, On Graphs with Equal Algebraic and Vertex Connectivity, Linear Algebra and its Applications 341 (2002), 45-56.
  • R. Bapat, S. Kirkland and S. Pati, The Perturbed Laplacian Matrix of a Graph, Linear and Multilinear Algebra 49 (2001), 219-242.
  • D. Gregory, D. Hershkowitz and S. Kirkland, The Spread of the Spectrum of a Graph, Linear Algebra and its Applications 332 (2001), 23-35.
  • S. Kirkland, An Upper Bound on Algebraic Connectivity for Graphs with Many Cutpoints, Electronic Journal of Linear Algebra 8 (2001), 94-109.
  • S. Kirkland, M. Neumann and J. Xu, A Divide and Conquer Approach to Computing the Mean First Passage Matrix for Markov Chains Via Perron Complement Reductions, Numerical Linear Algebra with Applications 8 (2001), 287-295.
  • S. Kirkland, J. Molitierno and M. Neumann, 57. The Sharpness of a Lower Bound on the Algebraic Connectivity for Maximal Graphs, Linear and Multilinear Algebra 48 (2001), 237-246.
  • S. Kirkland, P. Psarrakos and M. Tsatsomeros, On the Location of the Spectrum of Hypertournament Matrices, Linear Algebra and its Applications 323 (2001), 37-49.
  • C. Eschenbach, F. Hall, R. Hemasinha, S. Kirkland, Z. Li, B. Shader, J. Stuart and J. Weaver, Properties of Tournaments Among Well Matched Players, MAA Monthly December 2000, 881-892.
  • S. Kirkland and M. Neumann, Regular Markov Chain for which the Transition Matrix has Large Exponent, Linear Algebra and its Applications 361 (2000) 45-65.
  • S. Kirkland and M. Neumann, Extremal First Passage Times for Trees, Linear and Multilinear Algebra 48 (2000), 21-33.
  • S. Kirkland, D. Olesky and P. van den Driessche, Digraphs with Large Exponent, Electronic Journal of Linear Algebra 7 (2000), 30-40.
  • S. Kirkland, On the Sequence of Powers of a Stochastic Matrix with Large Exponent, Linear Algebra and its Applications 310 (2000), 109-122.
  • C. Eschenbach, F. Hall, R. Hemasinha, S. Kirkland, Z. Li, B. Shader, J. Stuart and J. Weaver, On Almost Regular Tournament Matrices, Linear Algebra and its Applications 306 (2000), 103-121.
  • S. Kirkland, A Bound on the Algebraic Connectivity of a Graph in Terms of the Number of Cutpoints, Linear and Multilinear Algebra 47 (2000), 93-103.
  • S. Kirkland and M. Neumann, On Group Inverses of M-matrices with Uniform Diagonal Entries, Linear Algebra and its Applications 296 (2000), 153-170.
  • S. Kirkland and M. Neumann, Cutpoint Decoupling and First Passage Times for Random Walks on Graphs, SIAM Journal on Matrix Analysis and Applications 20 (1999), 860-870.
  • S. Kirkland, Constructions for Type I Trees with Nonisomorphic Perron Branches, Czechoslovak Mathematical Journal 49 (1999), 617-632.
  • C. Eschenbach, S. Kirkland and J. Stuart, Irreducible Sign k-Potent Sign Pattern Matrices, Linear Algebra and its Applications 294 (1999), 85-92.
  • S. Kirkland, Perron Vector Ordering for a Subclass of Tournament Matrices, Linear Algebra and its Applications 291 (1999), 151-166.
  • D. Gregory and S. Kirkland, Singular Values for Tournament Matrices, Electronic Journal of Linear Algebra 5 (1999), 39-52.
  • S. Kirkland and S. Fallat, Perron Components and Algebraic Connectivity for Weighted Graphs, Linear and Multilinear Algebra 44 (1998), 131-148.
  • S. Kirkland, Review of `Nonnegative Matrices and Applications', by R.B. Bapat and T.E.S. Raghavan, Linear Algebra and its Applications 277 (1998), 357-360.
  • S. Kirkland, M. Neumann and B. Shader, On a Bound on Algebraic Connectivity: The Case of Equality, Czechoslovak Mathematical Journal 47 (1998), 65-76.
  • S. Kirkland, M. Neumann and B. Shader, Bounds on the Subdominant Eigenvalue Involving Group Inverses with Applications to Graphs, Czechoslovak Mathematical Journal 47 (1998), 1-20.
  • S. Fallat and S. Kirkland, Extremizing Algebraic Connectivity Subject to Graph Theoretic Constraints, The Electronic Journal of Linear Algebra 3 (1998), 48-74.
  • S. Kirkland and M. Neumann, The M-Matrix Group Inverse Problem for Weighted Trees, SIAM Journal on Matrix Analysis and Applications 19 (1998), 226-234.
  • S. Kirkland and D. Tasci, A Sequence of Upper Bounds for the Perron Root of a Nonnegative Matrix, Linear Algebra and its Applications 273 (1998), 23-28.
  • S. Kirkland, M. Neumann and B. Shader, Applications of Paz's Inequality to Perturbation Bounds for Markov Chains, Linear Algebra and its Applications 268 (1998), 183-196.
  • S. Kirkland, M. Neumann and B. Shader, Distances in Weighted Trees and Group Inverses of Laplacian Matrices, SIAM Journal on Matrix Analysis and Applications 18 (1997), 827-841.
  • S. Kirkland, A Note on Perron Vectors for Almost Regular Tournament Matrices, Linear Algebra and its Applications 266 (1997), 43-47.
  • S. Kirkland and M. Neumann, Algebraic Connectivity of Weighted Trees Under Perturbation, Linear and Multilinear Algebra 42 (1997), 187-203.
  • S. Kirkland, Perron Vector Bounds for a Tournament Matrix with Applications to a Conjecture of Brualdi and Li, Linear Algebra and its Applications 262 (1997), 209-227.
  • L.B. Beasley and S. Kirkland, On the Exponent of a Primitive Matrix Containing a Primitive Submatrix, Linear Algebra and its Applications 261 (1997), 195-205.
  • E. Dedo, S. Kirkland and N. Zagaglia Salvi, A Particular Class of Bigraphs, Ars Combinatoria 45 (1997), 13-28.
  • S. Kirkland, A Note on the Eigenvalues of a Primitive Matrix with Large Exponent, Linear Algebra and its Applications 253 (1997), 103-112.
  • S. Kirkland and with N. Pullman, The Polytope of Generalized Tournament Matrices with a Common Integral Score Vector,Ars Combinatoria 44 (1996), 3-22.
  • S. Kirkland, J. McDonald and M. Tsatsomeros, Sign-Patterns which Require a Positive Eigenvalue, Linear and Multilinear Algebra 41 (1996), 199-210.
  • S. Kirkland, A Note on the Sequence of Brualdi-Li Matrices, Linear Algebra and its Applications 248 (1996), 233-240.
  • S. Kirkland, On the Minimum Perron Value for an Irreducible Tournament Matrix, Linear Algebra and its Applications 244 (1996), 277-304.
  • S. Kirkland, M. Neumann and B. Shader, Characteristic Vertices of Weighted Trees Via Perron Values, Linear and Multilinear Algebra 40 (1996), 311-325.
  • Y. Chen, S. Kirkland and M. Neumann, Nonnegative Alternating Circulants Leading to M-Matrix Group Inverses, Linear Algebra and its Applications 233 (1996), 81-97.
  • S. Kirkland, The Group Inverse Associated with an Irreducible Periodic Nonnegative Matrix, SIAM Journal on Matrix Analysis and Applications 16 (1995), 1127-1134.
  • Y. Chen, S. Kirkland and M. Neumann, Group Generalized Inverses of M-Matrices Associated with Periodic and Nonperiodic Jacobi Matrices, Linear and Multilinear Algebra 39 (1995), 325-340.
  • L. Beasley, S. Kirkland and B. Shader, Rank Comparisons, Linear Algebra and its Applications 221 (1995), 171-188.
  • R. Hartwig and S. Kirkland, A Convexity Result for Complex Numbers with Applications to Nonnegative Normal Matrices,Linear Algebra and its Applications 221 (1995), 195-204.
  • S. Kirkland and M. Neumann, Group Inverses of M-matrices Associated with Nonnegative Matrices Having Few Eigenvalues, Linear Algebra and its Applications 220 (1995), 181-213.
  • S. Kirkland, Spectral Radii of Tournament Matrices Whose Graphs are Related by an Arc Reversal, Linear Algebra and its Applications 217 (1995), 179-202.
  • D. Gregory, S. Kirkland and N. Pullman, A Bound on the Exponent of a Primitive Matrix Using Boolean Rank, Linear Algebra and its Applications 217 (1995), 101-116.
  • D. Gregory, S. Kirkland and N. Pullman, On the Dimension of the Algebra Generated by a Boolean Matrix, Linear and Multilinear Algebra 38 (1994), 131-144.
  • S. Kirkland and M. Neumann, Convexity and Concavity of the Perron Root and Vector of Leslie Matrices with Applications to Population Models, SIAM Journal on Matrix Analysis and Applications 15 (1994), 1092-1107.
  • S. Kirkland and B. Shader, Tournament Matrices with Extremal Spectral Properties, Linear Algebra and its Applications 196 (1994), 1-17.
  • S. Kirkland and B. Shader, On Multipartite Tournament Matrices with Constant Team Size, Linear and Multilinear Algebra 35 (1993), 49-63.
  • D. Gregory, S. Kirkland and B. Shader, Pick's Inequality and Tournaments, Linear Algebra and its Applications 186 (1993), 15-36.
  • S. Kirkland, A Reversal Index for Tournament Matrices, Linear and Multilinear Algebra 34 (1993), 343-352.
  • S. Kirkland and N. Pullman, Linear Operators Preserving Invariants of Nonbinary Boolean Matrices, Linear and Multilinear Algebra 33 (1993), 295-300.
  • D. Gregory, S. Kirkland and N. Pullman, Power Convergent Boolean Matrices, Linear Algebra and its Applications 179 (1993), 105-117.
  • S. Kirkland, On the Spectrum of a Leslie Matrix with a Near Periodic Fecundity Pattern, Linear Algebra and its Applications 178 (1993), 261-279.
  • S. Kirkland and N. Pullman, Boolean Spectral Theory, Linear Algebra and its Applications 175 (1992), 177-190.
  • D. de Caen, D. Gregory, S. Kirkland, J. Maybee and N. Pullman, Algebraic Multiplicity of the Eigenvalues of a Tournament Matrix, with Linear Algebra and its Applications 169 (1992), 179-193.
  • D. Gregory, S. Kirkland and N. Pullman, Row-stochastic Matrices with a Common Left Fixed-vector, Linear Algebra and its Applications 169 (1992), 131-149.
  • S. Kirkland, An Eigenvalue Region for Leslie Matrices, SIAM Journal on Matrix Analysis and Applications 13 (1992), 507-529.
  • S. Kirkland, Hypertournament Matrices, Score Vectors and Eigenvalues, Linear and Multilinear Algebra 30 (1991), 261-274.

    Refereed Conference Proceedings

  • M. de Freitas, R. Del Veccio, N. Abreu and S. Kirkland, On Q-Spectral Integral Variation, Electronic Notes in Discrete Mathematics 35 (2009), 203-208.
  • A. Zappavigna, P. Colaneri, S. Kirkland and R. Shorten, A Scaling and Squaring Method for the Discretisation of Positive Switched Systems, Proceedings of the 2011 50th IEEE Conference on Decision and Control and European Control Conference (2011), 40844089.

    Book Chapters and Encyclopaedia Articles

  • S. Kirkland, Graph Structure Revealed by Spectral Graph Theoretic Methods, in Lectures on Matrix and Graph Methods, R. Bapat, S. Kirkland, K. Prasad and S. Puntanen, Eds., Manipal University Press, 2012, pp. 35-42.
  • E. Crisostomi, A. Schlote, S. Kirkland and R. Shorten, Markov Chain-based Emissions Models: a Precursor for Green Control, in Green IT: Technologies and Applications, J. Kim and M. Lee, Eds., Sringer-Verlag, 2011, pp. 381-400.
  • S. Kirkland, Matrix Operations, in The Encyclopaedia of Measurement and Statistics, N. Salkind, Ed., Sage Publishers, 2007, pp. 574-575.
  • S. Kirkland, Algebraic Connectivity, in Handbook of Linear Algebra, L. Hogben, R. Brualdi, A. Greenbaum and R. Mathias, Eds., CRC Press, 2006, pp. 36-1 to 36 -12.
  • S. Kirkland, Leslie Matrix, in The Kluwer Encyclopaedia of Mathematics Supplement II, Kluwer Academic Publishers (2000), 307-308.