I'm reading Linear Algebra by Bill Jacob and am having trouble with his development of the theory behind the right inverse of a matrix. I did an internet search but didn't find anything useful. Does anyone know of a reference that might explain the concept a little more clearly?
[Math] Right Inverse of a matrix
linear algebramatricesreference-request
Related Solutions
As it was suggested before, Module Theory: An Approach to Linear Algebra by T. S. Blyth is an awesome title which covers almost every basic topic of Module theory in a very elegant, clear and efficient way. It is hands down my favorite text in the subject, but unfortunately it has been long out of print and therefore it is expensive and hard to obtain.
I contacted T. S. Blyth a few months ago looking for the possibility of a new edition, or at least, for a Dover reprint or something like that. Recently, Tom told me that he just finished an electronic edition, and I inmediately helped him with a careful and exhausting typo hunting. With great joy, I shall let you all know that this venerable text is now available for free!
Best Answer
To find a left inverse of a square matrix, you would perform row operations, and keep account of each operation by performing the corresponding operation to the identity matrix, and multiplying the result on the left of the given matrix. Each row operation is applied to the left and the composition of these (applied to the identity matrix) is a right inverse for your given matrix provided the reduced row echelon form is the identity.
By analogy a right inverse would correspond to a sequence of column operations. You can figure out what a column reduction is even if it doe not make algorithmic sense to do this. Later you will learn that the right inverse is the left inverse. Try for a few small (2x2) or (3x3) examples.