Mathematics for AI and Machine Learning

Foundations for modern AI and machine learning

Weyl Bounds

Chapter 7 Linear algebra

Chapter 7: Symmetric Matrix — Weyl's Inequality

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Weyl Bounds — high-resolution mind-map icon

From the book

Chapter 7: Symmetric Matrix. In the chapter mind map this icon labels Weyl's Inequality: Eigenvalue Bounds of Sums. The discussion below is excerpted and lightly edited from § Theorem: Eigenvalue Bounds of Sums in Mathematics for AI and Machine Learning.

Let $A,B\in\mathbb{R}^{N\times N}$ be symmetric. All eigenvalues of $A+B$ lie in $[\lambda_{\min}(A+B), \lambda_{\max}(A+B)]$, and

What this drawing shows

What you see. Represents eigenvalue perturbation bounds that relate spectrum changes to matrix perturbations.

In the mind map. Chapter 7 — Weyl's Inequality: Eigenvalue Bounds of Sums. See From the book above for definitions, figures, and worked examples.

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Read the full definitions, figures, and worked examples in Chapter 7: Symmetric Matrix — see the mind-map node Weyl's Inequality: Eigenvalue Bounds of Sums.