| # QR decomposition: examples Matrices > QR decomposition > Examples Consider the matrix This matrix is full column rank. Indeed, the matlab command `[Q,R]=qr(A,0)` yields a and a : This shows that is full column rank since is invertible. The command `[Q,R]=qr(A)` actually produces the full QR decomposition, with now a orthogonal matrix: We can see what happens when the input is not full column rank: for example let's consider the matrix ( is not full column rank, as it was constructed so that the last column is a combination of the first and the third.) The (full) QR decomposition now yields: We observe that the last triangular element is virtually zero, and the last column is seen to be a linear combination of the first and the third. This shows that the rank of (itself equal to the rank of ) is effectively .