ThmDex – An index of mathematical definitions, results, and conjectures.
Result R5619 on D5858: Diagonal complex matrix
Subresult of R5620:
Formulation 0
Let $A \in \mathbb{C}^{2 \times 2}$ be a D6159: Complex square matrix such that
(i) \begin{equation} A = \begin{bmatrix} 1 & 2 \\ 2 & 4 \end{bmatrix} \end{equation}
(ii) \begin{equation} \Lambda = \begin{bmatrix} 2 & 0 \\ 0 & 1 \end{bmatrix} \end{equation}
Then \begin{equation} A \Lambda = \begin{bmatrix} 2 & 2 \\ 4 & 4 \end{bmatrix} \end{equation}
Proofs
Proof 0
Let $A \in \mathbb{C}^{2 \times 2}$ be a D6159: Complex square matrix such that
(i) \begin{equation} A = \begin{bmatrix} 1 & 2 \\ 2 & 4 \end{bmatrix} \end{equation}
(ii) \begin{equation} \Lambda = \begin{bmatrix} 2 & 0 \\ 0 & 1 \end{bmatrix} \end{equation}
This result is a particular case of R5620: . $\square$