Mathematics and StatisticsJudi McDonald

Judi McDonald

  1. Professor, Tenure Track
Email Addressjmcdonald1@wsu.edu
LocationNeill 323

Biography

Professor Judi McDonald is a complete academic, passionate about research, education, and shared governance. Her research focuses on predicting properties based on patterns in linear algebraic structures. She is a co-author of an introductory linear algebra textbook who enthusiastically educates, mentors, and learns from students at all levels – first year through PhD. She has been active in shared governance by chairing the Faculty Affairs Committee and serving as chair-elect, chair, and past chair of the WSU Faculty Senate. She served two years as an associate dean of the Graduate School. She is currently the Faculty Regent on the Board of Regents of Washington State University.

Education

  • Ph.D. – 1993
    Mathematics, University of Wisconsin, Madison, Wisconsin

    • Specialization: Linear Algebra Research Supervisor: Hans Schneider
    • Major: Algebra Minors: Analysis, Business
  • M.A. – 1991
    Mathematics, University of Wisconsin, Madison, Wisconsin
  • B.Sc. – 1988
    Honours Mathematics, University of Alberta, Edmonton, Alberta
  • International Baccalaureate – 1984
    Armand Hammer United World College, Montezuma, New Mexico

Publications

TEXTBOOK

Judi McDonald is a co-author of the top-selling introductory linear algebra textbook worldwide and created the interactive electronic version where figures and examples come alive.

  • David C. Lay, Steven R. Lay, and Judi J McDonald, Linear Algebra and its Applications, Sixth Edition.
  • David C. Lay, Steven R. Lay, and Judi J McDonald, Linear Algebra and its Applications, Sixth Edition – Interactive Electronic Version.
  • Judith J McDonald, Instructor’s Solutions Manual for Linear Algebra and its Applications, Sixth Edition.
  • David C. Lay and Judith J McDonald, Study Guide for Linear Algebra and its Applications, Sixth Edition.
  • David C. Lay, Steven R. Lay, and Judi J McDonald, Linear Algebra and its Applications, Fifth Edition.
  • David C. Lay, Steven R. Lay, and Judi J McDonald, Linear Algebra and its Applications, Fifth Edition – Interactive Electronic Version.
  • Judith J McDonald, Instructor’s Solutions Manual for Linear Algebra and its Applications, Fifth Edition.
  • David C. Lay and Judith J McDonald, Study Guide for Linear Algebra and its Applications, Fifth Edition.
  • David C. Lay, Judith J McDonald, and Thomas Polaski, Instructor’s Solutions Manual for Linear Algebra and its Applications, Fourth Edition.
  • David C. Lay and Judith J McDonald, Study Guide for Linear Algebra and its Applications, Fourth Edition.
  • Contributor to Linear Algebra and its Applications, Fourth Edition, by David C. Lay

REFEREED JOURNAL PUBLICATIONS

Dr McDonald’s research focuses on properties of linear algebraic systems and matrices that can be determined from patterns in the observed structures and more recently, linear algebra education.

  • McDonald, Stewart, and Harel (2024). A Student-Centered Lesson on Eigenvalues and Eigenvectors. PRIMUS. (pp. 1-16).
  • Peffer, McDonald, and Stewart (2024). Using CAS to promote students’
    ways of thinking through observation and conjectures: The case of eigenvalues and eigenvectors. Proceedings of the 26th Annual Conference on Research in Undergraduate
    Mathematics Education    . (pp. 1164-1169).
  • Peffer, McDonald, and Stewart (2023). Incorporating digital interactive figures: Facilitating student exploration into properties of eigenvalues and eigenvectors. Proceedings of the 28th Asian Technology Conference in Mathematics (ATCM). (pp. 342–351).
  • Basha and McDonald (2023). An extension of the numerical range over finite fields. Linear Algebra and its Applications, 673, 14-27.
  • Alanazi and McDonald (2023). Realizable Regions for the Symmetric Nonnegative Inverse Eigenvalue Problem for 6×6 Matrices. Linear and Multilinear Algebra, 1-19.
  • Basha and McDonald (2022). Orthogonality over finite fields. Linear and Multilinear Algebra, Vol 70, Issue 22, 7277-7289.
  • Stewart, Axler, Beezer, Boman, Catral, Harel, McDonald, Strong, Wawro (2022). The Linear Algebra Curriculum Study Group (LACSG 2.0) Recommendations. Notices of the American Mathematical Society. May; 69(5).
  • McDonald, Nandi, and Sivakumar (2022). Group inverses of matrices associated with certain graph classes. Electronic Journal of Linear Algebra, pp 204-220.
  • McDonald and Paparella (2021). A short and elementary proof of Brauer’s theorem. The Teaching Of Mathematics, 24(2), pp.85-86.
  • McDonald, Nandi, Sivakumar, Sushmitha, Tsatsomeros, Wendler, & Wendler (2020). M-matrix and Inverse M-matrix Extensions. Special Matrices, Vol. 8, pp. 186-203.
  • Hudelson, McDonald, & Wendler (2019). α-Adjacency: A generalization of adjacency matrices. The Electronic Journal of Linear Algebra, 35, 365-375.
  • Al Baidani and McDonald (2019). On the Block Structure and Frobenius Normal Form of Powers of Matrices. The Electronic Journal of Linear Algebra, 35, 297-306.
  • Glassett & McDonald (2019). Spectrally arbitrary patterns over rings with unity. Linear Algebra and Its Applications, Vol 576, 228-245.
  • McDonald & Melvin (2017). Spectrally arbitrary zero–nonzero patterns and field extensions. Linear Algebra and Its Applications, 519, 146-155.
  • McDonald & Paparella (2016). Matrix roots of imprimitive irreducible nonnegative matrices. Linear Algebra and Its Applications, 498, 244–261.
  • McDonald & Paparella (2016). Jordan chains of h-cyclic matrices. Linear Algebra and Its Applications, 498, 145-159.
  • McDonald, Paparella & Tsatsomeros (2014). Matrix Roots of Eventually Positive Matrices. Linear Algebra and Its Applications, 456,122-137.
  • Bodine & McDonald (2012). Spectrally Arbitrary Zero-Nonzero Patterns over the Finite Fields. Linear & Multilinear Algebra, 3(60), 285-299.
  • DeAlba, Grout, Kim, Kirkland, McDonald & Yielding (2012). Minimum rank of powers of trees. Electronic Journal of Linear Algebra, 23, 151-163.
  • McDonald & Yielding (2012). Complex spectrally arbitrary zero-nonzero patterns. Linear & Multilinear Algebra. 1(60), 11-26.
  • Bodine, Deaett, McDonald, Olesky & van den Driessche (2012). Sign Patterns that Require or Allow Particular Refined Inertias. Linear Algebra and Its Applications, 437, Issue 9, 2228- 2242.
  • Cavers, Cioaba, Fallat, Gregory, Haemers, Kirkland, McDonald & Tsatsomeros (2012). Skew-adjacency matrices of graphs. Linear Algebra and Its Applications, 436, Issue 12, 4512-4529.
  • Jeon, McDonald & Stuart (2011). The minimum upper bound on the first ambiguous power of an irreducible ray pattern.  Linear Algebra and Its Applications, 435, Issue 5, 1147-1156.
  • Eubanks & McDonald (2009). On a generalization of Soules matrices.  J. Matrix Anal. & Appl., 31, 1227-1234.
  • McDonald & Morris (2008). Level characteristics corresponding to peripheral eigenvalues of a nonnegative matrix.  Linear Algebra and Its Applications, 429(7), Pages 1719-1729.
  • McDonald & Stuart (2008). Spectrally arbitrary ray patterns. Linear Algebra and Its Applications, Vol. 429, Issue 4, 727-734.
  • DeAlba, Hentzel, Hogben, McDonald, Mikkelson, Pryporova, Shader & Vander Meulen (2007). Spectrally arbitrary patterns: reducibility and the 2n Linear Algebra and Its Applications, Vol. 423, Issue 2-3, 262-276.
  • Corpuz & McDonald (2007). Spectrally arbitrary zero-nonzero patterns of order 4. Linear and Multilinear Algebra, 55, No. 3, 249-274.
  • Kim, McDonald, Olesky & van den Driessche (2007). Inertias of zero-nonzero patterns. Linear and Multilinear Algebra, 55, No. 3, 229-238.
  • Li & McDonald (2006). Inverses of M-type matrices created with irreducible eventually nonnegative matrices. Linear Algebra and Its Applications, 419, Issue 2-3, 668-674.
  • Edwards, McDonald & Tsatsomeros (2005). On Matrices with common invariant cones with applications to neural and gene networks.  Special Issue on Mathematical Biology, Linear Algebra and Its Applications, 398, 37-67.
  • Britz, McDonald, Olesky & van den Driessche (2004). Minimal spectrally arbitrary sign patterns.  SIAM J. Matrix Anal. Appl., 26, no. 1, 257-271.
  • Carnochan Naqvi & McDonald (2004). Eventually nonnegative matrices are similar to semi-nonnegative matrices.  Linear Algebra and Its Applications, 381, 245-258.
  • Loewy & McDonald (2004). The symmetric nonnegative inverse eigenvalue problem for 5×5 matrices. The Positivity Issue of Linear Algebra and Its Applications, 393, 275-298.
  • McDonald, Psarrakos & Tsatsomeros (2004). Almost skew-symmetric matrices. Rocky Mountain Journal of Mathematics, 34, no. 1, 269-288.
  • McDonald (2003). The peripheral spectrum of a nonnegative matrix.  Linear Algebra and Its Applications, 363:  217-235.
  • McDonald, Olesky, Tsatsomeros & van den Driessche (2003). On the spectra of striped sign patterns.  Linear and Multilinear Algebra, 51, no. 1, 39-48.
  • Zaslavsky & McDonald (2003). A characterization of Jordan canonical forms which are similar to eventually nonnegative matrices with the properties of nonnegative matrices.    Linear Algebra and Its Applications, 372, 253-285.
  • Carnochan Naqvi & McDonald (2002). The combinatorial structure of eventually nonnegative matrices. Electronic Journal of Linear Algebra, 9, 255-269.
  • Knudsen & McDonald (2001). A note on the convexity of the realizable set of eigenvalues for nonnegative symmetric matrices. Electronic Journal of Linear Algebra, 8, 110-114.
  • Orzech, Hillel, Brown, Stewart, Dubiel, Taylor, McDonald, and Sookochoff (2001). Considering How Linear Algebra is Taught and Learned. Canadian Mathematics Education Study Group Groupe Canadien D’etude En Didactique Des Mathematiques, p.31.
  • McDonald and Neumann (2000). The Soules approach to the inverse eigenvalue problem for nonnegative symmetric matrices of order n ≤ 5.  Contemporary Mathematics, Vol 259, pp. 387-390.
  • Lee, McDonald, Shader, and Tsatsomeros (2000). Extremal properties of ray-nonsingular matrices.  Discrete Mathematics, 216, 221-233.
  • McDonald, Nabben, Neumann, Schneider & Tsatsomeros (1998). Inverse tridiagonal Z-matrices. Linear and Multilinear Algebra, Vol. 45, no. 1, 75-97.
  • Krupnik & McDonald (1998). Hereditary properties of matrices.  Linear and Multilinear Algebra, 45, no. 1, 1-17.
  • McDonald, Olesky, Schneider, Tsatsomeros & van den Driessche (1998). Z-Pencils. Electronic Journal of Linear Algebra, Vol 4, 32-38.
  • J. McDonald and H. Schneider (1998). Block LU factorizations of M-matrices.  Numerische Mathematik, 80, 109-130.
  • McDonald, Olesky, Tsatsomeros & van den Driessche (1997). Ray patterns of matrices and nonsingularity.  Linear Algebra and Its Applications, 267, 359-373.
  • Kirkland, McDonald &Tsatsomeros (1996). Sign patterns that require positive eigenvectors.  Linear and Multilinear Algebra, 41, no. 3, 199-210.
  • McDonald, Neumann, Schneider & Tsatsomeros (1996). Inverses of unipathic M-matrices. SIAM Journal on Matrix Analysis and Application, 17(4), 1035-1036.
  • McDonald, Neumann, Schneider & Tsatsomeros (1995). Inverse M-Matrix inequalities and generalized ultrametric matrices. Linear Algebra and Its Applications, Vol. 220, 321-341.
  • McDonald (1994). A product index theorem with applications to splittings of M-matrices. Linear Algebra and Its Applications, Vol 197-198, 511-530.
  • McDonald, Neumann & Schneider (1993). Resolvents of minus M-matrices and splittings of M-matrices. Linear Algebra and Its Applications, Vol 195, 17-34.
  • McDonald (1993). Partly zero eigenvectors and matrices which satisfy Au = b.  Linear and Multilinear Algebra, 33, 163-170.
  • Haxel, McDonald & Thomason (1987). Counting interval orderings. Order 4, 269-272 (1987).

OTHER PUBLICATIONS

  • Pamphlet on Mathematical Careers for the Canadian Mathematical Society.
  • Poster and website on Mathematical Careers for the Canadian Mathematical Society.
  • Judith J. McDonald and J. Harley Weston, Friezing at Washington State University, Mathematics Notes from Washington State University, (2003).
  • Chris Fisher, Allen Herman, Denis Hanson, Judith McDonald and Harley Weston, Math 101 – Introductory Finite Mathematics 1, an in-house published textbook at the University of Regina (2001).
  • Judith J. McDonald and J. Harley Weston. University of Regina Website. CMS Notes, Vol. 33, No. 5, (2001).
  • Karen Arnason, Judith J. McDonald, Mhairi (Vi) Maeers, and J. Harley Weston.  Interweaving Mathematics and Indigenous Cultures. Proceedings of the International Conference on New Ideas in Mathematical Education, (2001).