3. Matrix Diagonalization

Steps to Diagonalize a Matrix

Step 4: Construct the Diagonal Matrix D

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To construct the Diagonal Matrix place the eigenvalues of the original matrix A along its main diagonal
All other entries in D are zeros.
λ₁ = 5 and λ₂ = 1 therefore we construct the matrix D as follows

Eigenvectors and Matrix P

\[\Large \textcolor{purple}{D} = \begin{bmatrix} \textcolor{red}{1} & 0 \\ 0 & \textcolor{blue}{-5} \end{bmatrix} \]

note: The order of the eigenvalues in D must match the order of their corresponding eigenvectors in P

MCQ on Matrix Diagonalization

Which of the following statements correctly describes the construction of the diagonal matrix D?

Matrix D is formed by placing the eigenvectors of A along its diagonal. Matrix D is constructed by placing the eigenvalues of A along its main diagonal. Matrix D is a diagonal matrix with all its entries as zeros. Matrix D is formed by placing the eigenvalues of A in its rows.

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Steps to Diagonalize a Matrix

Step 4: Construct the Diagonal Matrix D

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