I have three habitat metrics (bathymetry, distance to seagrass, distance to mangroves) at different locations and would like to create a (Euclidean) similarity matrix.
If your data were cast as categorical and in raster format, then you could use Combine—Help | ArcGIS for Desktop. If your data are from tabular sources or from a table in a featureclass/shapefile, then reclassification and categorization is indeed possible. There are simple solutions depending upon you level of comfort with existing arcmap tools, your available license, and/or you willness to work outside arcmap in numpy, scipy, pandas, matlab etc etc.
So you first task is to determine whether you are looking for a parametric or non-parametric statistical analysis, or simply a visual first approximation of spatial associations. From there you could consider some of the tools in the spatial statistics toolset as a 2nd goto.
Can you give us unfamiliar with the term "Euclidean similarity matrix" a simple description of what you're looking for? One sentence or less, please
Retrieving data ...