ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Alphabet
Deduction system
Theory
Zermelo-Fraenkel set theory
Set
Binary cartesian set product
Binary relation
Map
Operation
N-operation
Binary operation
Enclosed binary operation
Groupoid
Ringoid
Semiring
Ring
Left ring action
Module
Linear combination
Linear map
Eigenvector
Matrix eigenvector
Complex matrix eigenvector
Definition D5977
Real matrix eigenvector
Formulation 0
Let $A \in \mathbb{R}^{N \times N}$ be a D6160: Real square matrix.
A D5200: Real column matrix $x \in \mathbb{R}^{N \times 1} \setminus \{ \boldsymbol{0} \}$ is an eigenvector for $A$ if and only if \begin{equation} \exists \, \lambda \in \mathbb{C} : A x = \lambda x \end{equation}
Results
R5086: Eigenvectors for a symmetric real matrix are orthogonal