ThmDex – An index of mathematical definitions, results, and conjectures.
Determinant of a scaled real matrix
Formulation 0
Let $A \in \mathbb{R}^{N \times N}$ be a D6160: Real square matrix such that
(i) $\lambda \in \mathbb{R}$ is a D993: Real number
Then \begin{equation} \text{Det}(\lambda A) = \lambda^N \text{Det}(A) \end{equation}
Proofs
Proof 0
Let $A \in \mathbb{R}^{N \times N}$ be a D6160: Real square matrix such that
(i) $\lambda \in \mathbb{R}$ is a D993: Real number
This result is a particular case of R5068: Determinant of a scaled complex matrix. $\square$