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I'm finishing up a matrix multiplication problem for an ASA paper and
have run into a question that has stumped me.
I have two bimodal binary matrices, one for 1980 and one for 1985. They
are conformable, with actors on rows and practices on columns. I want
to multiply the first (1980) by the transpose of the second (1985-T) to
get a count of frequency overlap ("M") between the two years. This
produces an asymmetric matrix ("M") because, while the number of actors
are the same for both years, the number of ties vary. I want to
multiply the new matrix ("M") by the inverse of the row sum of the
earlier 1980 matrix to get a percentage of ties retained across years.
Problem 1: The new product is also asymmetric and I am unable to
determine how to read this with regards to time. That is, since the off
diagonal cells are asymmetric, how do I determine if the flow from 1980
to 1985 is on the upper or lower diagonal?
Problem 2: Should I multiply "M" by the *transpose* of the inverted row
sum or just the inverted row sum? This is a simple question for a
single year *symmetric* matrix, (which simply produces the transpose of
the former). However these two vectors produce quite different results
in the asymmetric multi-year matrix.
Any help is appreciated.
Department of Sociology
University of California
Santa Barbara, CA 93106-9430
We shall not cease from exploration
And the end of all our exploring
Will be to arrive where we started
And know the place for the first time.
- T.S. Eliot, Little Gidding
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