Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Books
  3. A Concise Text on Advanced Linear Algebra
  • Cited by 3
  • Yisong Yang, Polytechnic School of Engineering, New York University
Publisher:
Cambridge University Press
Online publication date:
December 2014
Print publication year:
2014
Online ISBN:
9781316103845
DOI:
https://doi.org/10.1017/CBO9781316103845
Subjects:
Mathematics, Physics and Astronomy, Mathematical Methods, Algebra
Information

Book description

This engaging textbook for advanced undergraduate students and beginning graduates covers the core subjects in linear algebra. The author motivates the concepts by drawing clear links to applications and other important areas, such as differential topology and quantum mechanics. The book places particular emphasis on integrating ideas from analysis wherever appropriate. For example, the notion of determinant is shown to appear from calculating the index of a vector field which leads to a self-contained proof of the Fundamental Theorem of Algebra, and the Cayley–Hamilton theorem is established by recognizing the fact that the set of complex matrices of distinct eigenvalues is dense. The material is supplemented by a rich collection of over 350 mostly proof-oriented exercises, suitable for students from a wide variety of backgrounds. Selected solutions are provided at the back of the book, making it suitable for self-study as well as for use as a course text.

Refine List

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

Contents

Contents
References
Bibliographic notes
References
[1] G., Akemann, J., Baik, and P., Di Francesco, The Oxford Handbook of Random Matrix Theory, Oxford University Press, Oxford, 2011.
[2] G. W., Anderson, A., Guionnet, and O., Zeitouni, An Introduction to Random Matrices, Cambridge University Press, Cambridge, 2010.
[3] Z., Bai, Z., Fang, and Y.-C., Liang, Spectral Theory of Large Dimensional Random Matrices and Its Applications to Wireless Communications and Finance Statistics, World Scientific, Singapore, 2014.
[4] R. B., Bapat, Linear Algebra and Linear Models, 3rd edn, Universitext, Springer-Verlag and Hindustan Book Agency, New Delhi, 2012.
[5] C. W. J., Beenakker, Random-matrix theory of quantum transport, Reviews of Modern Physics 69 (1997) 731–808.
[6] R., Bellman, Introduction to Matrix Analysis, 2nd edn, Society of Industrial and Applied Mathematics, Philadelphia, 1997.
[7] A., Berman and R. J., Plemmons, Nonnegative Matrices in the Mathematical Sciences, Society of Industrial and Applied Mathematics, Philadelphia, 1994.
[8] M., Berry, S., Dumais, and G., O'Brien, Using linear algebra for intelligent information retrieval, SIAM Review 37 (1995) 573–595.
[9] R. A., Brualdi and H. J., Ryser, Combinatorial Matrix Theory, Encyclopedia of Mathematics and its Applications 39, Cambridge University Press, Cambridge, 1991.
[10] B. N., Datta, Numerical Linear Algebra and Applications, 2nd edn, Society of Industrial and Applied Mathematics, Philadelphia, 2010.
[11] E., Davis, Linear Algebra and Probability for Computer Science Applications, A. K. Peters/CRC Press, Boca Raton, FL, 2012.
[12] P., Diaconis, Patterns in eigenvalues: the 70th Josiah Willard Gibbs lecture, Bulletin of American Mathematical Society (New Series) 40 (2003) 155–178.
[13] G. H., Golub and J. M., Ortega, Scientific Computing and Differential Equations, Academic Press, Boston and New York, 1992.
[14] J., Gomide, R., Melo-Minardi, M. A., dos Santos, G., Neshich, W., Meira, Jr., J. C., Lopes, and M., Santoro, Using linear algebra for protein structural comparison and classification, Genetics and Molecular Biology 32 (2009) 645–651.
[15] A., Graham, Nonnegative Matrices and Applicable Topics in Linear Algebra, John Wiley & Sons, New York, 1987.
[16] F. A., Graybill, Introduction to Matrices with Applications in Statistics, Wadsworth Publishing Company, Belmont, CA, 1969.
[17] T., Guhr, A., Müller-Groeling, and H. A., Weidenmiiller, Random-matrix theories in quantum physics: common concepts, Physics Reports 299 (1998) 189–425.
[18] P. R., Halmos, Finite-Dimensional Vector Spaces, 2nd edn, Springer-Verlag, New York, 1987.
[19] K., Hoffman and R., Kunze, Linear Algebra, Prentice-Hall, Englewood Cliffs, NJ, 1965.
[20] K. J., Horadam, Hadamard Matrices and Their Applications, Princeton University Press, Princeton, NJ, 2007.
[21] R. A., Horn and C. R., Johnson, Matrix Analysis, Cambridge University Press, Cambridge, New York, and Melbourne, 1985.
[22] P., Lancaster and M., Tismenetsky, The Theory of Matrices, 2nd edn, Academic Press, San Diego, New York, London, Sydney, and Tokyo, 1985.
[23] S., Lang, Linear Algebra, 3rd edn, Springer-Verlag, New York, 1987.
[24] G., Latouche and R., Vaidyanathan, Introduction to Matrix Analytic Methods in Stochastic Modeling, Society of Industrial and Applied Mathematics, Philadelphia, 1999.
[25] P. D., Lax, Linear Algebra and Its Applications, John Wiley & Sons, Hoboken, NJ, 2007.
[26] W., Leontief, Input-Output Economics, Oxford University Press, New York, 1986
[27] Y. I., Lyubich, E., Akin, D., Vulis, and A., Karpov, Mathematical Structures in Population Genetics, Springer-Verlag, New York, 2011.
[28] M. L., Mehta, Random Matrices, Elsevier Academic Press, Amsterdam, 2004.
[29] C., Meyer, Matrix Analysis and Applied Linear Algebra, Society of Industrial and Applied Mathematics, Philadelphia, 2000.
[30] S. P., Meyn and R. L., Tweedie, Markov Chains and Stochastic Stability, Springer-Verlag, London, 1993; 2nd edn, Cambridge University Press, Cambridge, 2009.
[31] D. R., Stinson, Cryptography, Discrete Mathematics and its Applications, Chapman … Hall/CRC Press, Boca Raton, FL, 2005.
[32] J., Stoer and R., Bulirsch, Introduction to Numerical Analysis, Springer-Verlag, New York, Heidelberg, and Berlin, 1980.
[33] T., Tao, Topics in Random Matrix Theory, American Mathematical Society, Providence, RI, 2012.
[34] C. H., Taubes, Lecture Notes on Probability, Statistics, and Linear Algebra, Department of Mathematics, Harvard University, Cambridge, MA, 2010.
[35] P., Van Dooren and B., Wyman, Linear Algebra for Control Theory, IMA Voumes in Mathematics and its Applications, Springer-Verlag, New York, 2011.
[36] E., Wigner, Characteristic vectors of bordered matrices with infinite dimensions, Annals of Mathematics 62 (1955) 548–564.
[37] E., Wigner, On the distribution of the roots of certain symmetric matrices, Annals of Mathematics 67 (1958) 325–327.
[38] Y., Xu, Linear Algebra and Matrix Theory (in Chinese), 2nd edn, Higher Education Press, Beijing, 2008.

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Book summary page views

Total views: 0 *
Loading metrics...

* Views captured on Cambridge Core between #date#. This data will be updated every 24 hours.

Usage data cannot currently be displayed.