Definition:Eigenvector/Real Square Matrix

Definition

Let $\mathbf A$ be a square matrix of order $n$ over $\R$.

Let $\lambda \in \R$ be an eigenvalue of $\mathbf A$.

A non-zero vector $\mathbf v \in \R^n$ is an eigenvector corresponding to $\lambda$ if and only if:

$\mathbf A \mathbf v = \lambda \mathbf v$

Also see

• Definition:Eigenvalue of Real Square Matrix

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): eigenvalue
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): eigenvalue
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): eigenvalue, eigenvector