  Student's theorem is an important result in statistics which states that for
normal population, the sample variance is independent from the sample mean and
has a chi-square distribution. The existing proofs of this theorem either
overly rely on advanced tools such as moment generating functions, or fail to
explicitly construct an orthogonal matrix used in the proof. This paper
provides an elegant explicit construction of that matrix, making the algebraic
proof complete. The constructive algebraic proof proposed here is thus very
suitable for being included in textbooks.
