Introduction to Matrix Analysis

By Richard Bellman. 1972

Foreword Preface to the Second Edition Preface 1. Maximization, Minimization, and Motivation 2. Vectors and Matrices 3. Diagonalization and Canonical Forms for Symmetric Matrices 4. Reduction of General Symmetric Matrices to Diagonal Form 5. Constrained Maxima 6. Functions of Matrices 7. Variational Description of Characteristic Roots 8. Inequalities 9. Dynamic Programming 10. Matrices and Differential Equations 11. Explicit Solutions and Canonical Forms 12. Symmetric Function, Kronecker Products and Circulants 13. Stability Theory 14. Markoff Matrices and Probability Theory 15. Stochastic Matrices 16. Positive Matrices, Perron's Theorem, and Mathematical Economics 17. Control Processes 18. Invariant Imbedding 19. Numerical Inversion of the Laplace Transform and Tychonov Regularization Appendix A. Linear Equations and Rank Appendix B. The Quadratic Form of Selberg Appendix C. A Method of Hermite Appendix D. Moments and Quadratic Forms Index.

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Citations in the corpus

The Arrow of Time in Multivariate Time Series (2016, background): “To ensure a unique solution to (1) in the univariate case, one requires that (z) and ⇥(z) of the univariate ARMA(p, q) process (B)Xt = ⇥(B)✏t have no common zeros (Bellmann, 1987).”
Controlling for Individual Heterogeneity in Longitudinal Models, with Applications to Student Achievement (2007, background): “ω2 0(ω0+1) > 0. Theorem 3 on p. 116 of Bellman ( 7 ) states that if B1 and B2 are symmetric with B2 is positive semi-definite, then the smallest eigenvalue of B1 + B2 is greater than or equal to the smallest eigenvalue of B1. Letting B1 = and B2 = cωω′ gives that the smallest eigenvalue of”
Quantum feedback: theory, experiments, and applications (2014, methodology): “include the Kalman-Bucy filter [41] and the Hamilton-Jacobi -Bellman equation [42].”
Stability for time varying linear dynamic systems on time scales (2005, background): “We note that the time scale Lyapunov matrix equation is the uniﬁcation (with B(t) ≡ A T (t)) of the Sylvester matrix equation [3] XA(t) + B(t)X = − M for the case T = R and the Stein equation for the case T = Z .”
An Estimator for Some Binary-Outcome Selection Models Without Exclusion Restrictions (2003, background): “The characteristic roots of A⊗B are λiµi , where λi are the characteristic roots of A and µi are the roots of B (Bellman 1960, p. 227).”
Compact Spectral Bases for Value Function Approximation Using Kronecker Factorization (2007, methodology): “We adapted this theorem from a more general version (Bellman 1970) that does not place constraints on the two matrices.”
Multivariate stochastic volatility (2009, background): “2.5.1 Matrix Exponential Transformation Chiu et al. (1996) proposed a general framework for the logarithmic covariance matrix based on the matrix exponential transformation, which is well known in the mathematics literature (see, for example, Bellman (1970)).”
Generalized cross-validation as a method for choosing a good ridge parameter (1979, unknown): “(See Bellman [7], Wahba [41].)”
Face recognition: A literature survey (2003, methodology): “Noting that the number of images M usually available for computing the covariance matrix of the data is much less than the row or column dimensionality of the covariance matrix, leading to singularity of the matrix, a standard method from linear algebra [46] is used that calculates only the M eigenv”
Peak quasisymmetric functions and Eulerian enumeration (2003, background): “Thus we can conclude that 2n+1 is an eigenvalue of the linear map #. Since # is indecomposable, the Perron-Frobenius theory of nonnegative matrices (see, e.g., [ 8, Chapter 16 ]) implies that 2n+1 is the largest eigenvalue of # on the finite-dimensional space �n+1.”