I know to find if a set of vectors are linearly indepenent I have to put them in a matrix and get the rref. if the rref == the identity matrix, then the vectors are linearl independent. but why? can ...

Let P and Q be two idempotents on a Hilbert space. In this note, we prove that the invertibility of the linear combination $\lambda_{1}P + \lambda_{2}Q$ is independent of the choice of $\lambda_{i}$, ...

We present an algorithm for computing exact expressions for the distribution of the maximum or minimum of an arbitrary finite collection of linear combinations of spacings or exponential random ...