Eigenvalues and Eigenvectors
Special vectors v associated with a linear transformation matrix A that maintain their spatial direction when operated on, scaled only by factor λ.
Governing formula
A v = λ v (where v ≠ 0)
SI unit
Linear Algebra Object
In depth
Eigenvectors define principal axes of transformation. In physics, diagonalizing matrices into eigenvector bases uncouples systems of differential equations into independent modes.
Examples in the real world
Finding principal axes of inertia in rigid body mechanics and principal stress directions in elasticity theory.