Documentation: LinearAlgebra.qr - mention that the matrix R is quadratic

[Smeargul]

While the standard definition of a triangular matrix is that it is quadratic, the dimensions do not fit, and especially if you do not check the matrix, but only its rows/columns, it is easy to overlook that R is automatically truncated.

[andreasnoack]

It's not always square

julia> qr(randn(2,4)).R
2×4 Array{Float64,2}:
 1.62531   1.15414    0.215677  -1.24148
 0.0      -0.115364  -0.94133    1.12214

[Smeargul]

I just realized how unhelpful my comment was. I'm sorry for that.

Consider the code:

A = [ 2  -1  0; 0   1  2; 1  -1  2; 3   0  0; 0   1  2]
LinearAlgebra.qr(A)

Then this is the output:

LinearAlgebra.QRCompactWY{Float64,Array{Float64,2}}
Q factor:
5×5 LinearAlgebra.QRCompactWYQ{Float64,Array{Float64,2}}:
 -0.534522   0.311872  -0.0404557  -0.769465    0.152669
  0.0       -0.545777  -0.404557   -0.32998    -0.65542
 -0.267261   0.428825  -0.768658    0.384733   -0.0763343
 -0.801784  -0.350857   0.28319     0.384733   -0.0763343
  0.0       -0.545777  -0.404557   -0.0547528   0.731754
R factor:
3×3 Array{Float64,2}:
 -3.74166   0.801784  -0.534522
  0.0      -1.83225   -1.32546
  0.0       0.0       -3.15554

So, in this case the 5x3 matrix A is being factored into a 5x5 Q, and a 3x3 R.
(The last two (zero-)rows of R are being dropped)

This behaviour of cause makes sense, as in an m,n matrix with m>n, the last m-n rows will always be zero.
I'd only like to add this to the documentation, "That in this case, and in this case only, exactly the last m-n rows are cut from the matrix R"
(i.e. if the rank of our m,n matrix is <n, we'll still have that R is an n,n matrix, this time having zero rows)

[I'm also unsure why the matrix multiplication of an 5x5 and an 3x3 matrix works when using LinearAlgebra.qr(A).Q*LinearAlgebra.qr(A).R, while in general this would throw an error]

[andreasnoack]

It would be great if you could prepare a PR with the changes you think would be helpful.