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Exercise 1.5.6

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Suppose the columns of $P$ are $p_{1}, \dots, p_{n}$ , then we have $p_{i}^{T} p_{j} = 0$ if $i \neq j$ , and $1$ is $i = j$ . So $P^{T} P$ =I$ and $P$ is square so it’s orthogonal.

$P$ is orthogonal, so $P^{T} P = I$ and $P^{- 1} = P^{T}$ .

When a matrix is symmetric or orthogonal, it will have orthogonal eigenvectors.

niuers

2020-03-20 00:00

Exercise 1.5.6

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