Rothstein’s Code Transformations for Discordant Datasets: Matrix Operations

The Rothstein code is a binary vector representation of the slope of a line or scaling factor that was originally introduced for the scalar transformation of images. The methodology has built-in interpolation with each operation. The technique is underutilized for data operations and its use is amenable for the practical and real-world management of data from different sources, different data sampling methods, and discordant outputs from related processes. This work proposes and demonstrates the use of the code for assimilating data sets with discordant sizes for simple matrix operations. Examples presented are for the calculation of a matrix determinant, adding matrices, and matrix multiplication where the matrix sizes are untenable. The emphasis is on understanding the technique and its potential using simple examples, 2-dimensional matrices, and integer arithmetic.