The Net Advance of Physics:
MATRIX ALGEBRA

MATRICES:

• General: Introductory:
  • An Introduction to Business Mathematics by Henk van Elst [2015/09] "These lecture notes provide a self-contained introduction to the mathematical methods required in a Bachelor degree programme in Business, Economics, or Management:" i.e. linear algebra, matrix algebra, and single-variable calculus.

• General:
  • Analytical Methods in Physics by Yi-Zen Chu [2015] Textbook, 232 pp.
  • Méthodes Matricielles: Introduction à la Complexité Algébrique by Jounaïdi Abdeljaoued and Henri Lombardi [2016/04] 376 pp.
  • The Matrix Calculus You Need For Deep Learning by Terence Parr and Jeremy Howard [2018/02]
  • The eight epochs of math as regards past and future matrix computation by F. Uhlig [2020/08]

• General: NUMERICAL:
  • Sketching as a Tool for Numerical Linear Algebra by David P. Woodruff [Foundations and Trends in Theoretical Computer Science 10, 1 (2014)] 157 pp.
  • Literature survey on low rank approximations of matrices by N. Kishore Kumar and Jan Schneider [2016/06]
  • An Introduction to the Krylov Subspace Method by Shitao Fan [2018/11]
  • A Literature Survey of Matrix Methods for Data Science by M. Stoll [2019/12]
  • The eight epochs of math as regards past and future matrix computation by F. Uhlig [2020/08]

• Type: RANDOM;

• Type: ALTERNATING SIGN: Propp 2002/08;

• Type: DISTANCE:
  • Euclidean Distance Matrices: A Short Walk Through Theory, Algorithms and Applications by Ivan Dokmanic et al. [2015/02]

• Type: SYMMETRIC:
  • Symmetric Matrices: Theory and Applications by Helmut Kahl [2014/08]

• Aspects: EIGENVALUES:
  • Eigenvalue and Generalized Eigenvalue Problems: Tutorial by Benyamin Ghojogh et al. [2019/03] with some examples taken from machine-learning theory after a more general algebraic discussion.

• Aspects: INEQUALITIES:
  • Optimization on linear matrix inequalities for polynomial systems control by Didier Henrion [2013/05]
  • Linear Matrix Inequality Properties and Applications in Systems, Stability, and Control Theory by Ryan James Caverly and James Richard Forbes [2019/03]

• Re: COMPLEXITY:
  • Méthodes Matricielles: Introduction à la Complexité Algébrique by Jounaïdi Abdeljaoued and Henri Lombardi [2016/04] 376 pp.
  • Interactions of Computational Complexity Theory and Mathematics by Avi Wigderson [2017/10]

• Re: DIFFERENTIAL EQUATIONS:
  • Infinitesimal symmetry transformations of matrix-valued differential equations by Costas J. Papachristou [2018/04]

THE NET ADVANCE OF PHYSICS