Eigenvalues and eigenvectors

In this shear mapping the red arrow changes direction but the blue arrow does not. The blue arrow is an eigenvector of this shear mapping because it doesn't change direction, and since its length is unchanged, its eigenvalue is 1.

Matrix A acts by stretching the vector x, not changing its direction, so x is an eigenvector of A.

In linear algebra, an eigenvector or characteristic vector of a linear transformation is a non-zero vector that does not change its direction when that linear transformation is applied to it. In other words, if v is a vector that is not the zero vector, then it is an eigenvector of a linear transformation T if T(v) is a scalar multiple of v. This condition can be written as the equation

单词	Algebraic Multiplicity
释义	Algebraic Multiplicity 英语百科 Eigenvalues and eigenvectors In linear algebra, an eigenvector or characteristic vector of a linear transformation is a non-zero vector that does not change its direction when that linear transformation is applied to it. In other words, if v is a vector that is not the zero vector, then it is an eigenvector of a linear transformation T if T(v) is a scalar multiple of v. This condition can be written as the equation
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Algebraic Multiplicity

Eigenvalues and eigenvectors