Background Data from thousands of transcription-profiling experiments in organisms ranging from yeast to humans are now publicly available. How best to analyze these data remains an important challenge. A variety of tools have been used for this purpose, including hierarchical clustering, self-organizing maps and principal components analysis. In particular, concepts from vector algebra have proven useful in the study of genome-wide expression data. Results Here we present a framework based on vector algebra for the analysis of transcription profiles that is geometrically intuitive and computationally efficient. Concepts in vector algebra such as angles, magnitudes, subspaces, singular value decomposition, bases and projections have natural and powerful interpretations in the analysis of microarray data. Angles in particular offer a rigorous method of defining 'similarity' and are useful in evaluating the claims of a microarray-based study. We present a sample analysis of cells treated with rapamycin, an immunosuppressant whose effects have been extensively studied with microarrays. In addition, the algebraic concept of a basis for a space affords the opportunity to simplify data analysis and uncover a limited number of expression vectors to span the transcriptional range of cell behavior. Conclusions This framework represents a compact, powerful and scalable construction for analysis and computation. As the amount of microarray data in the public domain grows, these vector-based methods are relevant in determining statistical significance. These approaches are also well suited to extract biologically meaningful information in the analysis of signaling networks.