A classic problem in the field of pattern recognition is that of handwritten digit recognition. The heart of the problem lies within the ability to design an efficient algorithm that can recognize digits written and submitted by users via a tablet, scanner, and other digital devices. Previous studies have shown that the digits can be modeled as points in a high dimensional space which can adequately approximated by linear structures. In Chapters 2 and 3, we present two previously established algorithms rooted in two distinct geometric frameworks. In Chapter 4, we introduce a novel approach to the problem based on the linear structure that arises for the Grassmann manifold. From this framework, we developed three separate algorithms. We then tested our algorithms on the publicly available MNIST database and benchmarked our results with the algorithm described in Chapters 2 and 3. Without any preprocessing of the images, one of the Grassmann-based algorithms simultaneously achieved the highest classification rate and one of the fastest processing times.