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Zermelo-Fraenkel set theory
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Complex matrix determinant
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
»
R4962: Characteristic polynomial for a complex identity matrix
»
R5570: Special coefficients of complex matrix characteristic polynomial
»
R5559: Characteristic polynomial for a complex diagonal matrix
»
R5571: Complex algebra expression for the characteristic polynomial of a 2-by-2 complex square matrix
»
R5560: Characteristic polynomial for a triangular complex matrix
»
R5557: Complex matrix characteristic polynomial is a monic polynomial with degree equal to row and column dimensions
»
R5558: Characteristic polynomial for a complex diagonal matrix of constant diagonal
»
R5561: Characteristic polynomial for an upper triangular complex matrix
»
R5562: Characteristic polynomial for a lower triangular complex matrix