Synonym Characteristic vector of a linear transformation
Meaning An eigenvector is a nonzero vector that is changed at most by a scalar factor after the application of a linear transformation. It satisfies the formula Av = λv, where A is a matrix, λ is a scalar (eigenvalue) and v is the eigenvector.
Example This figure displays the matrix A acting on the vector x. The direction of the vector remains; thus, the x is the eigenvector of A.
Etymology German eigen (own), from adoptions or partial translations of German compounds in Mathematics and Physics.
