Question

Theorem 2.1 (Jordan Decomposition) Each symmetric matrix $A(p \times p)$ can be written as $A = \Gamma \Lambda \Gamma^T = \sum_{j=1}^{p} \lambda_j \gamma_j \gamma_j^T$ (2.18) where $\Lambda = diag(\lambda_1, ..., \lambda_p)$ and where $\Gamma = (\gamma_1, \gamma_2, ..., \gamma_p)$ is an orthogonal matrix consisting of the eigenvectors $\gamma_j$ of $A.$

          Theorem 2.1 (Jordan Decomposition) Each symmetric matrix $A(p \times p)$ can be
written as
$A = \Gamma \Lambda \Gamma^T = \sum_{j=1}^{p} \lambda_j \gamma_j \gamma_j^T$ (2.18)
where
$\Lambda = diag(\lambda_1, ..., \lambda_p)$
and where
$\Gamma = (\gamma_1, \gamma_2, ..., \gamma_p)$
is an orthogonal matrix consisting of the eigenvectors $\gamma_j$ of $A.$

Theorem 2.1 (Jordan Decomposition) Each symmetric matrix A(p × p) can be
written as
A = ΓΛΓ^T = ∑j=1^p^T (2.18)
where
Λ = diag(λ1, ..., )
and where
Γ = (γ1, γ2, ..., )
is an orthogonal matrix consisting of the eigenvectors of A.

Added by Christopher C.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Hubert Agamasu

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Start with a symmetric matrix A of size p x p. Show more…

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Theorem (Jordan Decomposition): Each symmetric matrix A (p x p) can be written as A = QDQ^T, (2.18) where D = diag(A1, A2, ..., Ap) and where Q is an orthogonal matrix consisting of the eigenvectors ~i of A.