Eigenvector Scaling
Chapter 6: Geometric Transformation and Eigen Decomposition — Definitions (also appears in Ch. 7)
From the book
Chapter 6: Geometric Transformation and Eigen Decomposition. In the chapter mind map this icon labels $A\mathbf{x}=\lambda\mathbf{x}$. The discussion below is excerpted and lightly edited from § Opening in Mathematics for AI and Machine Learning. Related material also appears in Chapter 7 (Real Eigenvalues $\lambda_i \in \mathbb{R}$ & Orthogonal Vectors).
Chapter 6: Geometric Transformation and Eigen Decomposition {-}
Geometric transformations, linear and affine mappings, and eigen decomposition
What this drawing shows
What you see. Shows an eigenvector keeping its direction while the matrix action scales it by an eigenvalue.
In the mind map. Chapter 6 — Eigenvector Scaling. See From the book above for definitions, figures, and worked examples.
Also appears in Ch. 7 (Real Eigenvalues & Orthogonal Vectors).
Where to read next
Read the full definitions, figures, and worked examples in Chapter 6: Geometric Transformation and Eigen Decomposition — see the mind-map node $A\mathbf{x}=\lambda\mathbf{x}$.
This concept is also referenced in Chapter 7 (Real Eigenvalues & Orthogonal Vectors).