Eigenvectors

Eigenvectors are special directions in a space where a transformation (like stretching or rotating) acts in a straightforward way. When you apply a linear transformation to an eigenvector, it changes only in magnitude, not in direction. Think of it like a spinning wheel: the points on the edge (eigenvectors) move along with the spin but don't change their basic orientation. In various fields, such as physics, computer graphics, and data analysis, eigenvectors help simplify complex problems by highlighting key directions of influence or variation within data or systems.