Matrix Analysis

Horn, R. A., & Johnson, C. R. (2012). Matrix Analysis. Cambridge University Press.

Type

Book

Intellectual base

Review or monograph

Year

2012

DOI

10.1017/cbo9781139020411

ISBN

9780521839402

DOI registrant

Cambridge University Press

Link

https://doi.org/10.1017/cbo9781139020411

Cited by

9 citations across 8 artifacts.

Each citation links to the sentence it supports in the citing article.

Domain-specific

• Bidiagonal matrix
  • The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
• Determinant
  • They are manifestations of the top exterior-power action induced by the same linear transformation.
• Exchange matrix
  • For dimension n, the exchange matrix J has entry one exactly when row plus column equals n plus one and zero otherwise; multiplying by it reverses the corresponding matrix axis.
  • The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
• Hurwitz-Stable Matrix
  • The preserved Wikipedia revision is discovery provenance only; the identity is grounded in standard linear-systems and matrix-analysis sources.
• Matrix
  • The spectral decomposition \(A = Q\Lambda Q^\top\) (for symmetric \(A\)) and the singular value decomposition \(A = U\Sigma V^\top\) (for any \(A\)) factor the matrix into geometrically interpretable pieces — rotations, reflections, scalings — that expose the principal directions of the transformation and their magnitudes

    This sourceThe standard graduate reference for these factorizations, organized around canonical forms and with sections on the singular value decomposition added in the second edition; its treatment is algebraic, so the reading of the factors as rotations, reflections and scalings is not taken from it.

    Supported in partVerified against the source

    Read by an automated reader; not a human review. How support was checked

• Matrix Similarity
  • This is precisely the change-of-basis relation: \(A\) and \(B\) are coordinate matrices of the same linear operator on an \(n\)-dimensional vector space, expressed in two ordered bases.
• Nonnegative Matrix
  • A matrix satisfying both conditions is often called doubly nonnegative.
• Transpositions matrix
  • The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.

Verification

Does it exist? Confirmed. This work's DOI resolves to a registered record, which fixes its identity. That is all it fixes.

Does it back the claim? Read against the text for 1 of 9 citations: 1 supported in part. Each verdict is shown under its citation below, with what in the work backs the sentence.

Support is checked per citation rather than per work — the same source can be cited soundly in one article and wrongly in another. Per-citation recording began recently, so a citation with no recorded check is a gap in the record rather than evidence it went unchecked.

See how references were verified.

Registry ID ref:dfd4c854f250 · see in the full table