Random Symmetric Matrices Are Almost Surely Nonsingular

Let Q(n) denote a random symmetric (n x n)-matrix, whose upper-diagonal entries are independent and identically distributed (i.i.d.) Bernoulli random variables (which take values 0 and I with probability 1/2). We prove that Q(n) is nonsingular with probability 1 - O (n (-1/8+delta)) for any fixed delta > 0. The proof uses a quadratic vers...More