dot product

For two n-dimensional real vectors P and Q, the operation s(P, Q) is defined as follows: $$s\left( {P,\;Q} \right) = \mathop \sum \limits_{i = 1}^n \left( {p\left[ i \right].Q\left...

For n > 2, let a {0, 1} n be a non-zero vector. Suppose that x is chosen uniformly at random from {0, 1} n . Then, the probability that $$\sum\limits_{i = 1}^n {{a_i}{x_i}} $$ is a...

The value of the dot product of the eigenvectors corresponding to any pair of different eigen values of a 4-by-4 symmetric positive definite matrix is ____________.