typically moves vectors in various directions. However, eigenvectors are special directions where the transformation only results in scaling (stretching or shrinking) rather than rotation. The eigenvalue represents the scale factor. 4. Practical Example Consider the matrix
Eigenvalues and eigenvectors act as the "DNA" of a matrix. By understanding these components, we can simplify high-dimensional problems, predict system stability, and extract meaningful patterns from complex datasets. Eigenvalues and Eigenvectors
: Eigenvectors define the principal axes of data variance, allowing for dimensionality reduction in machine learning. typically moves vectors in various directions