TITLE: Intuitive Difference between "square matrix with no inverse" vs non-square matrix ???
QUESTION [0 upvotes]: When we deal with square matrix $A$ of size $3\times 3$ and $\det(A)=0$, means our output after transformation lies in lesser dimensional space. Instead if deal with a non-square matrix $B$ of size $2\times 3$ means a 3D vector is transformed to 2D vector. What is the intuitive difference in the two formulations?

REPLY [0 votes]: In first case, the mapping is necessarily not onto. 
In  second case, it is not necessary that the mapping is onto.
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