- This is what makes up QR Decomposition!
- Q is a Orthogonal Matrix. (It has orthonormal column vectors!)
- R is a Upper Triangular Matrix
To get a QR decomposition:
- Take A, and apply the Gram-Schmidt process to the vectors inside it.
- Once you have found the orthonormal vectors of A, load them into a matrix by column. You now have Q
- Now, to find R. This is where some theory comes in.
- We have A and we have Q. We will multiply both sides of this equation to get
- Now, due to the properties of the orthogonal basis, and the orthonormal columns, we find this
- This leaves us with I. The I (identity matrix) is left on the right side!
- So, to find R, we just have to solve
Done! The R matrix has been solved for.
—