The dimensions of the matrix are important because a system of linear equations must be overdetermined- it must have more equations than unknowns in order to not have multiple perfect solutions, and in this case there are 360 equations and only 18 unknowns. The equations must be linearly independent- that is, each sample��s expression signature must not be the equal to the sum of other signatures when they are each multiplied by any constant- this requirement is also satisfied. Finally, the matrix must be well conditioned. That is, the Danshensu solutions yielded must be relatively stable and not overly sensitive to small fluctuations in input data. This characteristic represents a satisfactory bound on the error of the solution for a given mixture, and can be thought of as the result of a basis matrix that contains genes that together form a complete but parsimonious set of robust markers for the cell types of interest. The property of conditioning is quantified as the condition number, a positive Diperodon scalar value that is low when the matrix is stable. As expected, the condition number was found to be high for small or large numbers of genes and to have a minimum for moderate numbers of genes. The basis matrices used here were constructed in part by minimizing their condition number, and they do in fact have condition numbers near zero. The stability of the whole 
blood basis matrix was verified by comparing results of deconvolution of whole blood using all cell types to results obtained from deconvolution of the same samples with one or two of the cell types omitted. Omission of a few cell types did not grossly alter the results for the other cell types. Reassuringly, those that were altered were the ones that would be expected. For instance, omitting activated dendritic cells from the basis matrix caused resting dendritic cells to be estimated slightly higher in abundance since those two signatures are substantially similar. There are several limitations of microarray deconvolution that bear discussion. One is that it produces answers about the composition of a sample only for a given set of constituents, in this case the immune cell subset profiles that form the basis matrix. This set can be constructed beforehand or determined via bootstrap methods from the mixture data itself, but either way it may be incomplete or inaccurate.There are likely to be important subset conditioning of the matrix.