I would like to perform an Adonis / PERMANOVA test on my data. Adonis is more suited to be dataset as I have both continuous and categorical information however, understanding how to perform a PERMANOVA should also help me achieve what I need to do for Adonis. I think I understand the theory and would like to first perform an Adonis in QIIME and then in R. However, I am a bit confused as to what the input matrix for the command is.

eg. in QIIME1 the script used would be compare_categories.py http://qiime.org/scripts/compare_categories.html

This is the definition given for the input file: -i, --input_dmThe input distance matrix. WARNING: Only symmetric, hollow distance matrices may be used as input. Asymmetric distance matrices, such as those obtained by the UniFrac Gain metric (i.e. beta_diversity.py -m unifrac_g), should not be used as input

I am not sure what the difference is between a symmetric, hollow distance matrix and an asymmetric distance matrix. If anyone would be able to help explain this is simple terms or visually it would be very much appreciated. I just want to make sure that I correctly input the data to the results are valid. The only distance matrices I think I have were created by beta_diversity.py.