Checking the criterion for the positive definiteness of a matrix

Question

The article Bounds for Elgenvalues Using Traces on page 482 has the following statement:

If $A$ is Hermitian, the inequality (2.36) shows that $A$ is positive definite when $$\frac{\mbox{Tr}(A)^2}{\mbox{Tr}(A^2)} > n-1$$

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Here is an example of a symmetric positive-definite Hermitian matrix of the 4th order, for which the indicated criteria are not met. Why?

Remarque: It is not entirely clear from the article what the parameter $f$ is, but this formula even got into Definite Matrix - Properties. I ask the help of experts in trying to figure it out and I will be grateful.

n=4

A = {{4, 10, 30, 100}, {10, 30, 100, 354}, {30, 100, 354, 1300}, {100, 354, 1300, 4890}};

HermitianMatrixQ[A];

Eigenvalues[A] // N;

Tr[A] && Tr[A]^2/Tr[MatrixPower[A, 2]] > n - 1;