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Cited by 4,642Matrix Theory and AlgorithmsAdvanced Combinatorial MathematicsRings, Modules, and Algebras

Matrix Analysis

Horn, Roger A., Johnson, Charles R.·2012·Cambridge University Press eBooks
DOI 10.1017/cbo9781139020411
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Abstract

Linear algebra and matrix theory are fundamental tools in mathematical and physical science, as well as fertile fields for research. This second edition of this acclaimed text presents results of both classic and recent matrix analysis using canonical forms as a unifying theme and demonstrates their importance in a variety of applications. This thoroughly revised and updated second edition is a text for a second course on linear algebra and has more than 1,100 problems and exercises, new sections on the singular value and CS decompositions and the Weyr canonical form, expanded treatments of inverse problems and of block matrices, and much more.

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Crossref · 10.1017/cbo9781139020411

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  • The differential equation dx(t)/dt = A x(t) has solution x(t) = e^{tA} c.

    “We know from matrix analysis (via the theory of matrix functions) that the differential equation in (45) has as solution [31, 32, 33]”

    From Fundamentals of quantum mechanics in Liouville space (2020) · cites this paper as [33]

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Authors
Horn, R. A., & Johnson, C. R.
Affiliations
Johns Hopkins University (US)
ORCID
Venue
Cambridge University Press eBooks
Publisher
Cambridge University Press
Published
2012-10-22
DOI
10.1017/cbo9781139020411
OpenAlex
W4229706427
Cited by
4,642
References
0
Citations by year
2026: 491 · 2025: 685 · 2024: 530 · 2023: 515 · 2022: 460 · 2021: 405 · 2020: 324 · 2019: 238 · 2018: 254 · 2017: 274 · 2016: 217 · 2015: 132 · 2014: 99 · 2013: 11 · 2012: 1
FWCI
12.93
Type
book
Language
en
Open access
closed
Licence
www.cambridge.org/core/terms (unspecified, 165 d)
Locations
Cambridge University Press eBooks (publishedVersion)
Topics
  • Physical Sciences › Computer Science › Computational Theory and Mathematics › Matrix Theory and Algorithms
  • Physical Sciences › Mathematics › Discrete Mathematics and Combinatorics › Advanced Combinatorial Mathematics
  • Physical Sciences › Mathematics › Algebra and Number Theory › Rings, Modules, and Algebras
Keywords
matrix analysis, canonical form, singular value decomposition, inverse problems, block matrices, linear algebra, matrix theory

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