mlvljr
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# 10 Comments

 Nov25 comment Proving that a right (or left) inverse of a square matrix is unique using only basic matrix operations Huh, that's nice! :) Feb18 comment Looking for insightful explanation as to why right inverse equals left inverse for square invertible matrices @JackSchmidt You'd probably be interested in math.stackexchange.com/questions/110336/… Feb17 comment Proving that a right (or left) inverse of a square matrix is unique using only basic matrix operations @Arturo That's what I was thinking to try, thanks! (Once again you help me :) ) Feb17 comment Proving that a right (or left) inverse of a square matrix is unique using only basic matrix operations But how do I deal with the left inverse? (Is there a simmetry I have overlooked?) Feb17 comment Proving that a right (or left) inverse of a square matrix is unique using only basic matrix operations @Arturo Thanks for keeping the comment. Feb17 comment Proving that a right (or left) inverse of a square matrix is unique using only basic matrix operations Whatever row operations we apply to A to get it into reduced row-echelon form, if the same row operations are applied to I, the resulting matrix will have no zero rows. Then, if and only if A is row-equivalent to I, there will be a single set of solutions (i.e. B's column values) for every equation A_*B=I_, where A_ and I_ are transformed A and I and denotes j column. If there's a zero row i in A_, there will be at least one such j that I_ has a non-zero element in row i, and thus the system of equations has no solution. Feb17 comment Proving that a right (or left) inverse of a square matrix is unique using only basic matrix operations Or is it really that exotic? Feb17 comment Proving that a right (or left) inverse of a square matrix is unique using only basic matrix operations The idea I've got is that since elementary transforms of I will never give a zero row, any matrix A which is not row-equivalent to I, will produce an unsolvable set of equations for at least one column of B in A*B = I. Hence, for that matrix equation to hold, A must be row-equvalent to I and thus there's only one B sufficing the equation. Feb14 comment General rules to keep an eye on division by zero when dealing with a system of equations @Nuxonic, thanks, I know of the pivoting method(s?) existence, though have not yet looked at it. Feb14 comment General rules to keep an eye on division by zero when dealing with a system of equations Ok, do we never loose solutions utilizing the divid-by-possibly-zero-and-check-later method?