- This is what makes up QR Decomposition!
is a Orthogonal Matrix. (It has orthonormal column vectors!)**Q**is a Upper Triangular Matrix**R**

To get a QR decomposition:

- Take
, and apply the Gram-Schmidt process to the vectors inside it.**A** - Once you have found the orthonormal vectors of
, load them into a matrix by column.**A**__You now have__**Q** - Now, to find
. This is where some theory comes in.**R**

- We have
and we have**A**. We will multiply both sides of this equation to get**Q**

- Now, due to the properties of the
*orthogonal basis,*and the*orthonormal columns*, we find this

- This leaves us with
. The**I**(identity matrix) is left on the right side!**I**

- So, to find R, we just have to solve

Done! The R matrix has been solved for.

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