ALMOST ORTHOGONAL SUBMATRICES OF AN ORTHOGONAL MATRIX

MARK RUDELSON

Abstract. Let A be an n × M matrix whose rows are orthonormal. Let A_{I} be a submatrix of A whose column indexes belong to the set I. Given ε > 0 we estimate the smallest cardinality of the set I, such that the operator A_{I} is an ε-isometry.