What is the condition that guarantees that a symmetric function K: X* X →R is a kernel function?

Question

What is the condition that guarantees that a symmetric function `K: X* X →R` is a kernel function?

Accepted Answer

`[K(X_i,X_j )]` is a positive semidefinite matrix ∀ i,j.

Answer

`[K(X_i,X_j )]` is a symmetric matrix ∀ i,j.

Answer

`[K(X_i,X_j )]` is an upper triangular matrix ∀ i,j.

Answer

`[K(X_i,X_j )]` is an identity matrix ∀ i,j.

Question from the Machine Learning Algorithms test