It is proved that the value of the determinant of a real symmetric matrix is equal to the product of its eigenvalues?

It is proved that the value of the determinant of a real symmetric matrix is equal to the product of its eigenvalues?

Real symmetric matrix without condition
The characteristic polynomial of a | a - λ e | = (λ 1 - λ) (λ 2 - λ). (λ n - λ)
When λ = 0, there is | a | = λ 1, λ 2... λ n
That is, the determinant of a is equal to the product of all its eigenvalues (multiple roots are counted by multiple numbers)

Elden Ring Premiere

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