The Theory of Matrices. By F R. Gantmacher. Two volumes, pp. 374 and 276. 1959. (Translated from the Russian by K. A. Hirsch; Chelsea Publishing Company, New York)

http://reuter.mit.edu/papers/reuter-robreg10.pdf

Highly accurate inverse consistent registration: a robust approach.

"Matrix Mathematics" is a reference work for users of matrices in all branches of engineering, science, and applied mathematics. This book brings together a vast body of results on matrix theory for easy reference and immediate application. Each chapter begins with the development of relevant background theory followed by a large collection of specialized results. Hundreds of identities, inequalities, and matrix facts are stated rigorously and clearly with cross references, citations to the literature, and illuminating remarks. Twelve chapters cover all of the major topics in matrix theory: preliminaries; basic matrix properties; matrix classes and transformations; matrix polynomials and rational transfer functions; matrix decompositions; generalized inverses; Kronecker and Schur algebra; positive-semidefinite matrices; norms; functions of matrices and their derivatives; the matrix exponential and stability theory; and linear systems and control theory. A detailed list of symbols, a summary of notation and conventions, an extensive bibliography with author index, and an extensive index are provided for ease of use. The book will be useful for students at both the undergraduate and graduate levels, as well as for researchers and practitioners in all branches of engineering, science, and applied mathematics.

/pdf/matrix-mathematics-theory-facts-and-formulas-with-8swhnd659u.pdf

Matrix Mathematics: Theory, Facts, and Formulas with Application to Linear Systems Theory

Visual domain adaptation aims to learn robust classifiers for the target domain by leveraging knowledge from a source domain. Existing methods either attempt to align the cross-domain distributions, or perform manifold subspace learning. However, there are two significant challenges: (1) degenerated feature transformation, which means that distribution alignment is often performed in the original feature space, where feature distortions are hard to overcome. On the other hand, subspace learning is not sufficient to reduce the distribution divergence. (2) unevaluated distribution alignment, which means that existing distribution alignment methods only align the marginal and conditional distributions with equal importance, while they fail to evaluate the different importance of these two distributions in real applications. In this paper, we propose a Manifold Embedded Distribution Alignment (MEDA) approach to address these challenges. MEDA learns a domain-invariant classifier in Grassmann manifold with structural risk minimization, while performing dynamic distribution alignment to quantitatively account for the relative importance of marginal and conditional distributions. To the best of our knowledge, MEDA is the first attempt to perform dynamic distribution alignment for manifold domain adaptation. Extensive experiments demonstrate that MEDA shows significant improvements in classification accuracy compared to state-of-the-art traditional and deep methods.

https://dl.acm.org/doi/pdf/10.1145/3240508.3240512

Visual Domain Adaptation with Manifold Embedded Distribution Alignment

Matrix functions are used in many areas of linear algebra and arise
in numerous applications in science and engineering.
The most common matrix function is the matrix inverse;
it is not treated specifically in this chapter,
but is covered in Section~1.5 and Section~51.3.
This chapter is concerned with general matrix functions as
well as specific cases such as matrix square roots,
trigonometric functions,
and the exponential and logarithmic functions.

Functions of matrices

The matrix sign function and computations in systems

Roots of real matrices

Spectral decomposition of a matrix using the generalized sign matrix

: The aspects of state of the practice modeling and identification of large space structures are discussed in this report. Methods of modeling a structures as well as identification procedures are presented along with data acquisition and processing requirements. Recommendations for developing algorithms for the task of space structure identification are given.

http://www.dtic.mil/dtic/tr/fulltext/u2/a173756.pdf

Identification of Large Space Structures on Orbit

A new method of finding the roots of the quadratic matrix equation A + BR + RC + RDR = 0 , where A , B , C , and D are n × n matrices is described in this paper. The method gives all roots of the equation when the eigenvalues of the characteristic matrix are distinct and a subset of the roots where the eigenvalues are repeated. The sign and Walsh functions are utilized in the root extraction algorithm.

Eugene D. Denman

Papers

The matrix sign function and computations in systems

Roots of real matrices

Spectral decomposition of a matrix using the generalized sign matrix

Identification of Large Space Structures on Orbit

A new solution method for quadratic matrix equations