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Exercise 1.7.10

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If $S$ is symmetric, then we have ${(A^{T} SA)}^{T} = A^{T} S^{T} A = A^{T} SA$ so $A^{T} SA$ is also symmetric. $S$ has a dimension of $m$ by $m$ , while $A^{T} SA$ has a dimension of $n$ by $n$ , so their eigenvalues are not equal to each other.

niuers

2020-03-20 00:00

Exercise 1.7.10

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