QR-Factorization

$$A = QR$$

Here, $A$ is an $m \times n$ matrix with linearly independent columns and $m > n$. Applying the Gram-Schmidt Process to the columns of $A$ and then normalizing these vectors yields $Q$. Then:

$R = Q^T A$.

$A = QR$ effectively expresses matrix $A$ as a linear combination of the orthonormal column vectors of $Q$ with the scalar components found in $R$, which is an upper triangular matrix.