Linear Algebra: Invertibility

What is Invertibility? What does that have to do with a matrix’s columns and shape?

• For a matrix to be invertible, it must represent a bijective transformation. In other words, for every vector in its codomain, there must be exactly one input vector that maps to it.




• The concept of range is relevant here, since, as its name suggests, the range
  
  
  $R(A)$
  
  of a matrix
  
  $A$
  
  is the set of vectors in the codomain that …

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