Proof: For every invertible matrix $A$ there is a permutation matrix $P$ and an invertible upper triangular matrix $R$ and $R'$, such that $A=R'PR$…
Can someone give me a hint? I dont even know where to start
Permutation matrix and invertible matrix
linear algebra
Best Answer
Hint: If you matrix has as $a_{11}$ entry zero permute the row with a non zero row. Now start doing gauss ellimination. Keep all the accounting in matrix forms. Remember multiplying a matrix from the left gives sou row combinations as gauss ellimination does. Multiplying from right gives you collumn combinations. Can you do a similar method to get your result? (A is invertible so its not a zero matrix and a diagonal matrix is also an upper traingular) .