Suppose A is any m by n matrix. A+ is a generalized inverse of A if A+ is n by m and AA+A = A. Then, a fundamental theorem for linear equations is: The equation, Ax = b, has a solution if, and only if, AA+b = b for any generalized inverse, A+ Found on http://glossary.computing.society.informs.org/index.php?page=G.html
Suppose A is any m by n matrix. A+ is a generalized inverse of A if A+ is n by m and AA+A = A. Then, a fundamental theorem for linear equations is: The equation, Ax = b, has a solution if, and only if, AA+b = b for any generalized inverse, A+