Eigenvalue and Eigenvector Calculator

An eigenvector of a square matrix A is a non-zero vector v that, when multiplied by A, yields a scaled version of itself. In other words, A multiplies the eigenvector v by a scalar value called the eigenvalue. It can be represented as:A * v = λ * v, where A is the matrix, v is the eigenvector, and λ (lambda) is the eigenvalue associated with that eigenvector.

Eigenvalues are the scalars that correspond to the eigenvectors of a matrix. They provide information about the behavior of transformations represented by the matrix. The eigenvectors indicate the directions along which the transformation stretches or compresses, while the eigenvalues represent the scaling factors for those directions.

Calculating eigenvalues and eigenvectors involves solving the characteristic equation, which is derived from the equation (A - λI) * v = 0, where I is the identity matrix.