References & Further Reading

References

1. G. Strang, Linear Algebra and Its Applications, Wellesley-Cambridge Press, 5th ed., 2019

   The standard undergraduate reference. Chapters 6–7 on eigenvalues and SVD are especially relevant.

2. R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, 2nd ed., 2012

   Definitive reference for eigenvalue inequalities, Kronecker products, and matrix functions. Our go-to for rigorous proofs.

3. D. Tse and P. Viswanath, Fundamentals of Wireless Communication, Cambridge University Press, 2005

   Appendix A covers the linear algebra prerequisites for MIMO. Our treatment goes deeper but follows the same spirit.

4. S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004. [Link]

   Appendix A is an excellent concise review of linear algebra with an optimization focus. Freely available online.

5. K. B. Petersen and M. S. Pedersen, The Matrix Cookbook, 2012. [Link]

   Indispensable cheat-sheet for matrix identities, derivatives, and Kronecker product properties. Keep this within reach.

6. G. H. Golub and C. F. Van Loan, Matrix Computations, Johns Hopkins University Press, 4th ed., 2013

   The bible of numerical linear algebra. Essential for understanding how eigenvalues, SVD, and least-squares are actually computed.

7. Å. Björck, Numerical Methods for Least Squares Problems, SIAM, 1996

   Deep dive into Gram-Schmidt, Householder, and Givens methods. Chapters 1–3 complement our treatment of orthogonalization.

8. İ. E. Telatar, Capacity of Multi-Antenna Gaussian Channels, European Transactions on Telecommunications, vol. 10, no. 6, pp. 585–595, 1999

   The foundational paper on MIMO capacity. Shows the SVD and water-filling from this chapter in their natural habitat.

Further Reading

• Numerical stability of Gram–Schmidt and alternatives

  L. N. Trefethen and D. Bau III, *Numerical Linear Algebra*, SIAM, 1997, Lectures 7\u20138

  Explains why Modified Gram\u2013Schmidt and Householder reflections are preferred in practice. Essential reading for anyone implementing these algorithms.

• Random matrix theory for massive MIMO

  R. Couillet and M. Debbah, *Random Matrix Methods for Wireless Communications*, Cambridge University Press, 2011, Ch. 2

  Bridges the deterministic linear algebra here to the statistical eigenvalue distributions that govern massive MIMO performance (covered in Ch. 18).

• Kronecker products in channel modeling

  W. Weichselberger et al., \u2018A stochastic MIMO channel model with joint correlation of both link ends,\u2019 IEEE Trans. Wireless Commun., vol. 5, no. 1, pp. 90\u2013100, Jan. 2006

  Original paper on the Kronecker channel model \u2014 uses everything from Section 1.7. Required reading before Chapter 18.

• Comprehensive matrix calculus reference

  J. R. Magnus and H. Neudecker, *Matrix Differential Calculus with Applications in Statistics and Econometrics*, 3rd ed., Wiley, 2019

  The most thorough treatment of matrix derivatives. Goes far beyond our essentials in Section 1.8, covering second-order derivatives and the commutation matrix.

• Matrix inequalities for information theory

  R. A. Horn and C. R. Johnson, *Topics in Matrix Analysis*, Cambridge University Press, 1991, Ch. 7

  Deeper treatment of Hadamard, Fischer, and Minkowski inequalities. These appear repeatedly in multi-user capacity regions (Ch. 20\u201322).

• SVD algorithms and implementations

  J. Demmel, *Applied Numerical Linear Algebra*, SIAM, 1997, Ch. 5

  Covers the Golub-Kahan bidiagonalization and divide-and-conquer SVD algorithms used by LAPACK/NumPy/MATLAB.