If \( f: T \to \R \) and \( f \) is thought of as a column vector indexed by \( T \), then \( K f \) is simply the ordinary product of the matrix \( K \) and the vector \( f \); the product is a colum...If \( f: T \to \R \) and \( f \) is thought of as a column vector indexed by \( T \), then \( K f \) is simply the ordinary product of the matrix \( K \) and the vector \( f \); the product is a column vector indexed by \( S \): \[K f(x) = \sum_{y \in S} K(x, y) f(y), \quad x \in S \] Similarly, if \( f: S \to \R \) and \( f \) is thought of as a row vector indexed by \( S \), then \( f K \) is simple the ordinary product of the vector \( f \) and the matrix \( K \); the product is a row vector…
