QR Decomposition (or QR factorization) of a matrix \(A\) is a decomposition into a product \(A = QR\).

• \(Q\) is an orthogonal matrix, meaning its columns are orthonormal vectors and \(Q^T Q = I\).
• \(R\) is an upper triangular matrix.

The Process (using Gram-Schmidt):

1. The columns of matrix \(A\) are treated as a set of vectors \(\{a_1, a_2, ..., a_n\}\).
2. The Gram-Schmidt process is applied to this set to produce an orthonormal set of vectors \(\{q_1, q_2, ..., q_n\}\). These vectors become the columns of matrix \(Q\).
3. The matrix \(R\) is then calculated using the formula \(R = Q^T A\).