10. Bibliography¶
Alsaqre, Falah. Two-Dimensional PCA for Face Recognition (https://www.mathworks.com/matlabcentral/fileexchange/69377-two-dimensional-pca-for-face-recognition), MATLAB Central File Exchange. Retrieved July 10, 2019.
Léon Autonne. Sur l’Hermitien. Rendiconti del Cireolo Matematico di Palermo, 16:104–128, 1902.
Brunton, Steven and Kutz, Nathan. Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control. Cambridge University Press, 2019.
Buffington, Garrett. Polar Decomposition of a Matrix. University of Puget Sound, 2014. http://buzzard.ups.edu/courses/2014spring/420projects/math420-UPS-spring-2014-buffington-polar-decomposition.pdf
Chamberlain, Andrew. The linear algebra view of the Fibonacci sequence. https://medium.com/@andrew.chamberlain/the-linear-algebra-view-of-the-fibonacci-sequence-4e81f78935a3, 2016.
Chapra, Steven C. and Canale, Raymond L. Numerical Methods for Engineers, Seventh Edition. McGraw-Hill, 2015.
Chen, Mei-Qin. A Brief History of Linear Algebra and Matrix Theory. The Citadel, 2012. http://www.macs.citadel.edu/chenm/240.dir/12fal.dir/history2.pdf
Cline, R.E. and Plemmons, R.J. l_2–Solutions to Undetermined Linear Systems. SIAM Review, Vol. 18, No. 1 (Jan., 1976), pp. 92-106. https://www.jstor.org/stable/2029001.
Corke, Peter. Robotics, Vision and Control – Fundamental Algorithms in MATLAB. Second Edition. Springer, 2017.
Peter Corke. Spatial math toolbox. https://petercorke.com/toolboxes/spatial-math-toolbox/, 2020.
Deisenroth, Marc Peter, et al. Mathematics for Machine Learning. Cambridge University Press, 2020.
Demmel, James W. Applied Numerical Linear Algebra. SIAM, 1997.
Demmel, James W. and Kahan, William. Accurate singular values of bidiagonal matrices. SIAM Journal on Scientific and Statistical Computing, 11(5):873–912, 1990.
A. A. Dubrulle. Householder Transformations Revisited. SIAM Journal on Matrix Analysis and Applications, 22(1):33–40, 2000.
Eckart, C. and Young, G. The approximation of one matrix by another of lower rank, Psychometrika, vol. 1, No. 3, 1936, pp. 211-218. doi:10.1007/BF02288367.
John G.F. Francis. The qr transformation a unitary analogue to the lr transformation – part 1. The Computer Journal, 4(3):265–271, 1961.
John G.F. Francis. The QR transformation – part 2. The Computer Journal, 4(4):332–345, 1962.
Gavish, M. and Donoho, D. L. The Optimal Hard Threshold for Singular Values is 4/sqrt(3), IEEE Transactions on Information Theory, vol. 60, no. 8, pp. 5040-5053, Aug. 2014, doi: 10.1109/TIT.2014.2323359.
Wallace Givens. Numerical computation of the characteristic values of a real symmetric matrix. Technical report, Oak Ridge National Lab.(ORNL), Oak Ridge, TN, 1954.
Wallace Givens. The characteristic value-vector problem. Journal of the ACM (JACM), 4(3):298–307, 1957.
Wallace Givens. Computation of Plane Unitary Rotations Transforming a General Matrix to Triangular Form. Journal of the Society for Industrial and Applied Mathematics, 6(1):26–50, 1958.
Golub, Gene H. and Kahan, William. Calculating the singular value decomposition and pseudo-inverse of a matrix. SIAM, 2(2):205–224, 1965.
Golub, G.H., Reinsch, C. Singular value decomposition and least squares solutions, Numer. Math. 14, 403–420, 1970. https://doi-org.er.lib.k-state.edu/10.1007/BF02163027
Golub, Gene H. and Van Loan, Charles F. Matrix Computations, 4th ed. Baltimore, MD: Johns Hopkins University Press, 2013,
Martin H. Gutknecht and Beresford N. Parlett. From qd to LR, or, how were the qd and LR algorithms discovered? IMA Journal of Numerical Analysis, 31(3):741–754, 05 2010.
C. R. Hadlock. Field Theory and Its Classical Problems, The Carus Mathematical Monographs. Mathematical Association of America, 1978.
Karl Hessenberg. Behandlung linearer eigenwertaufgaben mit hilfe der Hamilton-Cayleyschen gleichung. IPM, 1940.
Higham, Nicholas J. Gaussian elimination, Wiley Interdisciplinary Reviews: Computational Statistics, 3, pp. 230-238, 2011.
Higham, Nicholas J. Accuracy and Stability of Numerical Algorithms, Second Edition. SIAM, 2002.
Hogg, Robert V., and Craig, Allen T. Introduction to Mathematical Statistics, Fourth Edition. Macmillan, 1978.
Alston S. Householder. Principles of Numerical Analysis. McGraw-Hill, New York, 1953.
Alston S. Householder. Unitary Triangularization of a Nonsymmetric Matrix. Journal of the ACM, 5(4):339–342, 1958.
Alston S. Householder. The Theory of Matrices in Numerical Analysis. Blaisdell Publishing Company, New York, 1964.
Founders Online, National Archives. From George Washington to John Parke Curtis, 3 August 1778. https://founders.archives.gov/documents/Washington/03-16-02-0249
Institute of Electrical and Electronics Engineers Inc. James (jim) hardy wilkinson. https:https://history.computer.org/pioneers/wilkinson.html, 2013.
IEEE Standard for Binary Floating-Point Arithmetic, in ANSI/IEEE Std 754-1985, 12 Oct. 1985, pp.1-20. doi: 10.1109/IEEESTD.1985.82928.
Klein, Philip N. Coding the Matrix: Linear Algebra through Applications to Computer Science. Newtonian Press, 2013.
Kutz, Jose Nathan. Data-Driven Modeling & Scientific Computation: Methods for Complex Systems & Big Data. Oxford University Press, 2013.
Lambers, James. CME 335 Lecture 6 Notes, Stanford University, 2010. https://web.stanford.edu/class/cme335/lecture6.pdf
Carla D Martin and Mason A Porter. The extraordinary SVD. The American mathematical monthly, 119(10):838–851, 2012.
L. Mirsky. Symmetric Gauge Functions and Unitarily Invariant Norms. The Quarterly Journal of Mathematics, 11(1):50–59, 01 1960.
Tom Lyche. Numerical Linear Algebra and Matrix Factorizations, volume 22. Springer Nature, 2020.
Richard R. Mertz. Alston Scott Householder interview: July 20, 1970. In Computer Oral History Collection, page 47–es, USA, 1999. Smithsonian Institution Press.
Moler, Cleve. Professor SVD. A blog post in the MathWorks’ Technical Articles and Newsletters, 2006. https://www.mathworks.com/company/newsletters/articles/professor-svd.html
Moler, Cleve. Gil Strang and the CR Matrix Factorization, A blog post from Cleve’s Corner, 2020. https://blogs.mathworks.com/cleve/2020/10/23/gil-strang-and-the-cr-matrix-factorization/
Moore, David S. and Notz, William and Fligner, Michael. The Basic Practice of Statistics, W.H. Freeman and Co., New York, 2018.
J.J. O’Connor and E.F. Robertson. MacTutor biography of Issai Schur. https://mathshistory.st-andrews.ac.uk/Biographies/Schur/, October 1998.
WC Sangren. Mathematics panel semiannual progress report for period ending December 31, 1954. Technical report, Oak Ridge National Lab.(ORNL), Oak Ridge, TN, 1954.
AS Householder. Mathematics panel semiannual progress report for period ending June 30, 1956. Technical report, Oak Ridge National Lab.(ORNL), Oak Ridge, TN, 1956.
Corke, Peter. Robotics, Vision and Control – Fundamental Algorithms in MATLAB, Second Edition. Springer, 2017.
Issai Schur. ¨Uber die charakteristischen wurzeln einer linearen substitution mit einer anwendung auf die theorie der integralgleichungen. Mathematische Annalen, 66(4):488–510, 1909.
Strang, Gilbert. Linear Algebra MIT Course. MIT Open Courseware, 1999. https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/video-lectures/
Strang, Gilbert. Computational Science and Engineering. Wellesly-Cambridge Press, 2007.
Strang, Gilbert. Introduction to Linear Algebra, 5th Edition. Wellesly-Cambridge Press, 2016.
Strang, Gilbert. RES.18-010 A 2020 Vision of Linear Algebra. Massachusetts Institute of Technology: MIT OpenCourseWare, 2020. https://ocw.mit.edu.
Gilbert W Stewart. Introduction to matrix computations. Elsevier, 1973.
Stewart, G. W. On the Early History of the Singular Value Decomposition. SIAM Review 35, no. 4, 1993, pp 551–66. http://www.jstor.org/stable/2132388.
Tharwat, Alaa. PCA (Principal Component Analysis). (https://www.mathworks.com/matlabcentral/fileexchange/30792-pca-principal-component-analysis), MATLAB Central File Exchange. Retrieved July 12, 2019.
Tucker, Alan. The Growing Importance of Linear Algebra in Undergraduate Mathematics. The College Mathematics Journal, Vol. 24, No. 1, Jan., 1993, pp. 3-9.
Herbert Westren Turnbull and Alexander Craig Aitken. An introduction to the theory of canonical matrices. Blackie & son limited, London, 1932. Reprints in 1945 and 1948.
Gene Golub and Frank Uhlig. The QR algorithm: 50 years later its genesis by John Francis and Vera Kublanovskaya and subsequent developments. IMA Journal of Numerical Analysis, 29(3):467–485, 2009.
Watkins, David S. Fundamentals of Matrix Computations. John Wiley & Sons, third edition, 2010.
David S. Watkins. Francis’s algorithm. The American mathematical monthly, 118(5):387–403, 2011
Williams, Gareth. Linear Algebra with Applications, Eighth Edition. Jones & Bartlett Learning, 2014.
James H. Wilkinson. Stability of the reduction of a matrix to almost triangular and triangular forms by elementary similarity transformations. J. Assoc. Comput. Mach., 6:336–359, 1959.
James H. Wilkinson. The Algebraic Eigenvalue Problem. Clarendon Press, Oxford University, 1965.
James H. Wilkinson. Global convergence of tridiagonal QR algorithm with origin shifts. Linear Algebra and its Applications, 1(3):409–420, 1968.
Yang, Won Young, et al. Applied Numerical Methods Using MATLAB. John Wiley & Sons, 2005. doi: 10.1002/0471705195
Yeturu, Kalidas. Chapter 3 - Machine learning algorithms, applications, and practices in data science. Handbook of Statistics. Elsevier, Volume 43, 2020, pp. 81-206, https://doi.org/10.1016/bs.host.2020.01.002.
