Test your intuition: is the following true or false?
Assertion 1: If is a square matrix over a commutative ring , the rows of are linearly independent over if and only if the columns of are linearly independent over .
(All rings in this post will be nonzero commutative rings with identity.)
And how about the following generalization?
Assertion 2: If is an matrix over a commutative ring , the row rank of (the maximum number of -linearly independent rows) equals the column rank of (the maximum number of -linearly independent columns).
If you want to know the answers, read on…Continue reading