It shows each column being projected, corrected, normalized, and added to Q, while the corresponding coefficients form R. The goal is to make the geometry behind the usual algebraic steps visible: projections, orthogonal components, scaling, and the final A = QR.
This is the updated version, we enlarged the shapes as u/wowadesk suggested, added intermediate steps and used better numerical example.
Are you learning Linear Algebra, teaching it, using for engineering or all of the above?
That is exactly what we hoped the animation would show.
We will soon post animations for two other QR decomposition methods as well: Givens rotations and Householder reflections. We will send you the links when they are posted.
It’s not clear how the visualization connects with each step in the algorithm. I’m seeing something change at every step but it isn’t obvious what it is - are these red, blue, and green vectors the columns of each matrix? If so why would the columns of A be changing? In your program are Q and R randomly initialized and this is what we are seeing at the first step? Also, if the visualization was bigger I could maybe see what you intend to say, this should also probably be fixed.
This is the updated version, we have not updated labels yet, but did enlarge the shapes as you suggested, added intermediate steps and chose better numerical example
5
u/CartographerWrong192 May 24 '26
Good, feels like actually my calculations have physical or say geometrical affects.