Spectra and Pseudospectra

Trefethen, L. N., & Embree, M. (2005). Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators. Princeton University Press.

Type

Book

Intellectual base

Review or monograph

Year

2005

DOI

10.2307/j.ctvzxx9kj

ISBN

9780691213101

DOI registrant

Princeton University Press

Link

https://doi.org/10.1515/9780691213101

Cited by

3 citations across 3 artifacts.

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

Domain-specific

• Pseudospectrum
  • … between constitutive identity and a convenient observable transfers from A canonical example satisfies the full defining rule of Pseudospectrum with assumptions and conventions explicit. to A careful use of Pseudospectrum tests the constitutive rule and nearest confusable rather than relying on the label alone..

Mechanisms

• Eigendecomposition Workflow
  • For non-normal operators the eigenvectors can be nearly parallel and wildly ill-conditioned, so the tidy modal picture is numerically fragile, and — worse — the eigenvalues alone can hide large transient growth that erupts before the asymptotic decay the spectrum promises.

    This sourceShows that nonnormal systems can have ill-conditioned eigenvectors and large transient amplification even when their eigenvalues predict eventual decay.

• Full-Rank Eigendecomposition
  • A defective matrix has too few independent eigenvectors and simply has no eigenbasis

    This sourceShows why defective matrices lack an eigenbasis and why nonnormal eigenvectors can produce transient behavior that eigenvalues alone miss.

Verification

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Links previously used in the corpus

Before the registry existed this work was also linked 1 other way.

• https://doi.org/10.2307/j.ctvzxx9kj ×1

Registry ID ref:9a911a3d5b2e · see in the full table