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
Countable map
Array
Matrix
Square matrix
Set of square matrices
Matrix determinant
Complex matrix determinant
Definition D5825
Complex matrix characteristic polynomial
Formulation 0
Let $A \in \mathbb{C}^{N \times N}$ be a D6159: Complex square matrix.
The characteristic polynomial of $A$ is the D4881: Complex function \begin{equation} \mathbb{C} \to \mathbb{C}, \quad z \mapsto \text{Det}(z I_N - A) \end{equation}
Results
Characteristic polynomial for a complex diagonal matrix
Characteristic polynomial for a complex diagonal matrix of constant diagonal
Characteristic polynomial for a complex identity matrix
Characteristic polynomial for a lower triangular complex matrix
Characteristic polynomial for a triangular complex matrix
Characteristic polynomial for an upper triangular complex matrix